{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4-final"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python_defaultSpec_1600514604160",
   "display_name": "Python 3.7.4 64-bit ('base': conda)"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "source": [
    "# 手写识别的例子"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "digits = datasets.load_digits()\n",
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "noisy_digits = X + np.random.normal(0, 4, size=X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "example_digits = noisy_digits[y==0,:][:10]\n",
    "for num in range(1, 10):\n",
    "    X_num = noisy_digits[y==num,:][:10]\n",
    "    example_digits = np.vstack([example_digits, X_num])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 64)"
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "source": [
    "example_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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vhnl0dDTMS5Uq5XuOtWvX+jq+9PR0OI7rsfSHDx+GeXJyMsxPnDgB87p169I5GPb5mfFjzEkrVqyAeZkyZWCOHvmfKSYmhs0Bj7FgwYLhEiVKePZnnxU7r8x4S4czZ87AvFChQjB3taZh14YtW7b4OkfZOK6f7cmTJ2G+Y8cOmLP7HWvUqEHnOHv2LMy3bduWY+co+06Z8e8ua5OQnc8Q2bVrlyUlJcF+CwkJCeGyZct68ogI/O9s9jM049fY9evX+9rf9Rmyn+H69evpd7BkyZKe/dl3mZ27ZrxlBbteJiQkwJzNbWZ26tQpmG/dupWeo/Hx8WHUniJ37tx0Hob9/mStbtgxstwMrzX27dtnx44dgz9gXwuf8uXL2/Llyz0560vFeuKYmfXq1Qvm11xzDcxZ363+/fvTOdgPPDIyEt6tzo6PnThxcXF0bob1KKtcuTLMhw0bRsdiF+pSpUr5Or7ExEQ4jmtR+c4778B8wYIFMP/hhx9gjt7PpYRCIVptwI4xOxznD8xZv5oWLVrQOWrWrAlzdowlSpSwL774wpMXLlwYjoN6CmVq1KgRzFl/rxtvvBHmrj5Pc+fOhfkNN9zg6xxlPZhcP9uZM2fCvEuXLjBnn/e0adPoHH///TfM27Vrl2Pn6F9//UW3HT9+HOYdO3aEeXY+Q6RevXp0W9myZeF1gP1yXrt2LR2rQIECMEd9pMz492DOnDl0jmPHjsG8cuXK8DMsWbKkff311568evXqcBx27prxf5iw6yXrhciuI2Zmv/32G8zbtGlDz9HSpUvD875cuXJ0Hoado6wPW58+fWDOjt3s4iLnn9q2bUv31391iYiISGBo4SMiIiKBoYWPiIiIBIave3yOHTtmX331lSfv0aOH74m3bNkC8/Hjx8Oc/R/tbbfdRucoWrSo7/eFsHt51q1bR1/DbqxkNx3mzZsX5uweCTOz+vXr020Mui8oOzeIDxo0COavvfYazNm9Ba7/e7/hhht8vy9m586dMB89ejR9zfnz52HeqVMnmA8fPhzmAwYMuMS78wfdEFmsWDHf47AbXZs2bQrziRMnwtx1j8aVV17p+30h7F6eJUuW0New+yTYzcJRUVEwnzVrFp2jb9++dFtOadKkCd3Grk3oxlQzs9WrV+fIe3KJiIhw3mz7Txs2bKDbunbtCvO0tDSYHzp0COauG8Rd98EhsbGx9F5UpE2bNnTb22+/DfMPPvgA5uyGYHY/m9nF+wL9unDhArzBmt3jwwolzPhnsmjRIl+56x6flJQUT5aRkUH31198REREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMHxVdcXHx/uq4GJ3Z5vx6oLdu/HDJFllhetx536lp6fbkSNHPDmrDnNVjb3++uswb9asGczZ0y27d+9O5xgzZgzdxqCKoDVr1sB9XZ9fUlISzNlToJcuXQpzV+WWq1KASU1Ntb1793ryChUqwP1ZJZaZWb9+/WDOKkTY08hZiwQz/60CwuEwrDZjrV5cWNsE9iT2m2++GeasxYWZWfHixX2/L+Szzz6DOauGNHNXuiCs5UhOV26lp6fb0aNHPTl7cvT+/fvpWOxnz/IOHTpk4R3+J9Rm59y5c77HGTduHMwPHjxIX8Mqoljl4bx582Duesq+6/xFMjIyYBVRbGysr3Eyx0KefvppmLueVM64nurMxMTE2NVXX53l/V3nw+TJk2HOzsU8efJked5MVapU8TWO/uIjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGBo4SMiIiKBoYWPiIiIBIavcnYzXH7Hyn5d5dZ9+vSBOWuYuWvXLpi7msX9/vvvdBuSkpICS7v37dsH97/77rt9jW/Gm3uyckBXSTcrs2XN3DIyMmDpJmuUxxrGmpk1bNgQ5uzz89sI0MysWrVqvl+TO3duWpaMoPL+TB07doQ5K/Nk8xYuXDjL7+dS8uXLB5tW/vbbb3B/VoJuxr+37Od+3XXXwbxUqVJ0DlaGzhw7dsy+/fZbT37PPffA/V2fn1+uxw7kpMjISHhOTJ06Fe7/wAMP0LE+/vhjmM+YMQPm7HEaqDw7U9WqVT2Zq1SYlesXKFAA7u+6jrJtY8eOhTlroulqKO1qAotERETA0vX77rsP7u9qhMzUrl0b5uz77GrCmp1HD/jFzisz/iiRiAj8d5errroK5q7HHvhtxKq/+IiIiEhgaOEjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGD4quoKh8OWlpbmydld66672f1WY7DmlwkJCfQ1N954o6854uLirFWrVlne31WNcMUVV8D8nXfegfnIkSNhXrJkySy/n0uJiIiATR1ZNQKrDjMzmz9/Psznzp0Lc9Zk1tUgcOXKlXQbc/LkSZs+fbonv+WWW+D+rqrAV199Febsc2cNZfPnz0/n2LZtG93mR+vWrWHOGl+amU2cOBHmXbp0gfkbb7wBc9aE0Mzs0UcfhTmrSIyPj7c777zTk6PP1Mysffv2dG42R+/evWE+atQomC9fvpzOUa9ePbrNL1ZFyHKzi80kEVZJiBrcmvFqUzPcQNl1XrGqtc6dO8P9UWPoTK4mwsi0adNgfuWVV9LXbN261dcczB133AHzDRs20NewBrSsiTerkHJVdeVUo2Czi9dX5LbbbqOvYdt++OEHmK9atQrmqampl3h3Wae/+IiIiEhgaOEjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGD4quoKhUIWHR3tyYcOHQr3Z3egm/GqJ9aPI1++fDB33c3OXuMXq4QIh8P0NawPUvXq1WHO+vH079//Eu8u6/bv32/PPPOMJ2eVE6676FnFE6veYpVNqMosU9OmTek2pkCBArCC64svvoD7f//993SsypUrw3zRokUwr1OnDszZz8TMf+Uhs3HjRl+5Ga9CYX2CtmzZAvMDBw5c4t1lXUpKCqzqQP2izMx++uknOhY7fzt06ABzVpHIKqfMeAXK/wrrI8iqXe+66y6Yu84TVBGVK1cuuv+hQ4fszTff9OSsAu7666+nY23fvp1uQ9jPo2bNmvQ1S5Ys8TXH6dOnbfbs2Z68ZcuWcH9XpTCrdGO9Kdk5Xbp0aTpHTp6jrEfbuHHjfI/FKjKHDBkCc9aHzcxs/fr1nuzs2bN0f/3FR0RERAJDCx8REREJDC18REREJDC08BEREZHA0MJHREREAsNXVRfD7s5evHgxfY3f/iidOnWCOav2MDObOXOmrzlSUlJgjxRW5eLy6aefwrxKlSowZ/2DXFhlFVOqVClfvW9OnDhBt91+++0wZ9VbrHrqm2++oXN069bN8e6wtLQ0O3TokCdnP1/WE8eM99Fh5zur9sqpyi2XiAj8bxjWo8yM90Jj5yjrZcX6I2VHbGwsrY7zK3fu3DBfs2YNzMuXLw/zdevW0TkaNmzo+32dP38eXv9YpeukSZPoWKzK5vHHH4f50qVLYc4qc81whZGr4rNo0aL20EMPeXJXdRzz4osvwpydc3/99RfMb775ZjoH6g1nZtazZ0+YR0VFwR6Kripf5oYbboA5G4ud0y6ufoTM2bNnYaUUq+Zz9ULLyMjwNXeLFi187W9mVqNGDU/mOt/0Fx8REREJDC18REREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMHyVsycnJ9v8+fM9eXx8PNzf1WDz5MmTMH/66adhXqpUKZhv2LCBzuFXbGysr9J1V0lnVFQUzFnJLGui6Xo/jz32GMxRI1Kzi2W027Zt8+So/NvMXYbYoEEDmN9zzz0wL1CgAMxR09v/N6KioqxYsWJZ3r9IkSJ0GzvnUJmnmdlHH32U5XkznT592vdrkBIlSsDcVf7KvoNnzpyBOStzd3E1Ec4J7BjMzKZMmQJz9jN5+OGHYc4aX5qZ7dixw/HusIyMDNr4GDl+/Djddu+998KcNXrcu3cvzHPye5iammp79uzx5KwBtat8OS4uzvfcyLBhw+hr6tev72uOo0eP2vjx4z05+w6yRqRmvJz93LlzMJ8zZw7M27RpQ+dgDWtdYmJiYIm461xk/L6GXV/T0tLoa1iDWEZ/8REREZHA0MJHREREAkMLHxEREQkMLXxEREQkMLTwERERkcAI+WmsFgqFEs1s93/v7fzPlAuHw55yHh3fZQMen9m//xh1fJeNf/s5+m8/PjOdo5f7MfLjy05HWREREZHLkf6rS0RERAJDCx8REREJDC18REREJDB8tayIj48Ply5d2pO7Hovv14oVK2BesWJFmBcqVIiOxVourFq1Kgnd9JSQkBBGLSWOHDkCx4mNjaVzHz58GOaVKlWir8kpK1as8HV87PH5mzZtonOwn3v+/PlhnjdvXpi7WjYULlwY5uz4zMwKFCgQLl68uCe/cOECHCsmJobOn56eDnPWpqBatWowz5UrF53jwIEDMD98+DA8xsKFC4fLlSvn2T8iwv+/Ydij5NnxsfYe6Jpwqffl9xxlXG1V2LaNGzf62v/qq6/O8vvJ5DpH4+Pjw6gdSnbaRrAWDey8Onr0KMxdbQ3Qde7o0aOWnJwcQvsXKlQIHh9rwxAKwWHMjH8H8+TJA3N2zULfmUzsmrV+/focOUdd2Oe3bt06X+O4fq8ULFgQ5q5ztHDhwuGyZct6cvZ+Xa1b2PeqZMmSMGfXfRd0LUtMTLRTp07Bk8vXwqd06dI2Y8YMmOcU9iV49dVXYd6lSxc61tmzZ2EeGxsL71YvX768LV++3JN/8MEHcJxrrrmGzj1ixAiYT548mb4mp4RCIV/Ht3XrVjhOs2bN6By33Xabr9c0bNgQ5n/++Sedo2fPnjBnx2dmVrx4cfv44489+YkTJ+D+tWrVovMnJibCvHv37jD/5ZdfYM76lJnxnkpvvPEGPMZy5crBnxm7eLt89913MO/atSvMb7/9dpi/+eabdA624PV7jjKsr5gZ//7XrVsX5uwfAH7eTybXOVqqVCn76aefPHmFChV8z7Nr1y6YDx06FObjxo2DOfs+m+HvyOuvv073L1WqlE2aNMmTb9myBe7P+hqa8X90sn9kNG7cGObPPfccnYP1eapYsWKOnKMuu3fj08Tvwuqdd96h22699VaYu87RsmXLwr5grNfbnXfeSednC1527evVqxcdi0G/V5944gm6v/6rS0RERAJDCx8REREJDC18REREJDC08BEREZHA8HVzc2pqqu3Zs8eTs5ubv/zySzpW7969YV6sWDGYs5vAXFwVO34MGDAA5q5qhHfffRfmTz31FMwfeeQRmKMKpUysAs6vK664AuaHDh2ir/n6669hzipgIiPxqcZuUsyuPHny2FVXXeXJFyxYAPc/ePAgHeuBBx6A+dtvvw1zVjnywgsv0DnYTaJvvPEGzCMiInzdyDxr1iy6jd04umHDBpizG8F79OhB52A3m+YUdvO0mVmrVq1g3qdPH5i/9957ME9JSaFzuCo7mejoaHgj89KlS+H+rPrOjN+Az25iZl555RW6Dd2c+umnn9L9k5OTbd68eZ68UaNGcH9UPZTp2LFjMGc3qLPvLNvfLHs3lSP79++HOapwy8SuGawaklVIuT5vdnOzS0REBPz9uXr1arj/tm3b6FisMo/d7D527FiY33333XQOdHM+K4gy0198REREJEC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMHxVdYVCIfh4cda/g/XEMeN30qN2A2b8keqDBw+mc/y3jRw5km7r378/zF966SWYs+ot18+QPT7cr5UrV8K8b9++9DWjR4+GOat0C4fDMGf9WrIrMjIStoioV68e3H/hwoV0LPYZsnO3SZMmMGetHszM5s+fT7chaWlpsNqOPfafVTaZmX3zzTcwZ1WMrDrjuuuuo3Owz505f/48rBBhVZ2s3YAZPz5WSfPJJ5/A/KOPPqJz5OT1p0GDBr5f07FjR5jPnj0b5uznNXPmTDoHqtpztZlISEiwe++915OzzzAuLo6OhaqIzcxat24Nc/Z9Ym2HsmPv3r2wCpdV8roMHz4c5qx3GqvEnDp1Kp0jO8ceCoVgPzRWocba9ZiZ7dy5E+Y33ngjzFm7junTp9M5brnlFroN0V98RN9wehMAACAASURBVEREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMLTwERERkcDwVc6eN29eq1+/vidnJYSVKlWiY7GmeD179oR5dHQ0zOfOnUvnuP766+k25MKFC7AhYKFCheD+y5Yto2OxUughQ4bAnJW5s0ZuZryUlUlOTra//vrLkzdr1gzuf//999OxXI0T/7/EyjAXL14M99+6dSsd6/nnn4d59+7dYc4aKuZkI9aoqCj46APUFNKMNxA2448rYCW2jKsRql/s83OVrTOsbL1Dhw4wZ02NXSXr7BxxSU1NhaXd7LEStWvXpmOxMmb2WJBp06bB/OzZs3SOnMI+j/Pnz9PX1KhRA+asWeb27dthnpSUROdYtGgR3YaUKVMmW6XrbCzk1KlTMGcNpV2/J5KTk2E+cOBA+ppwOAyb07Lvoev38FtvvQVztgZg5e/s/DHDj1dxfeb6i4+IiIgEhhY+IiIiEhha+IiIiEhgaOEjIiIigaGFj4iIiASGr6ouhjVndDWgnDx5MsybNm3qa3+XEydO+No/LS3NDh8+7MlZVZereSETHx8Pc1ad4arc2rRpk6+58+XLByu4Hn30Ubj/sGHD6FisMa3fSjNWvWDmbl7InDx50mbMmOHJu3Tp4nusKlWqwPzJJ5+E+QMPPOB7Dr/C4TD82bPvjcvLL78M83HjxsF8ypQpMGfNBrMjd+7csBLtjz/+gPvv27ePjrV8+XKY//TTTzDfv3//pd/gP7CqLtd3JyMjw86cOePJq1evDvdfs2YNHevtt9+GOWsiys4TVtGWk1gDY1dl5Zw5c2COfn5mZmPGjIE5a/ppZta+fXu6DTl16pT9+uuvnpxVdXbr1o2O1atXL5i3a9cO5gsWLIB5SkoKnSNfvnx0G8OqKxlXM2LWnDYxMRHma9euhXmtWrXoHDVr1vRkn376Kd1ff/ERERGRwNDCR0RERAJDCx8REREJDC18REREJDC08BEREZHA8FXVlZGRAXu6fP7553D/7FS5/PzzzzBn/VwuXLhAx2J3+DNnz561v//+25OzXkuuSogGDRrAnN35z6qhXJUmfntAHT9+HFbHsZ5cgwYNomOxY9+2bZuv9+SqymFVLi4FChSwtm3benJWuTF9+nQ6FqoUMDPr1KkTzFnFnourogVJTU2F5wTrUdSqVSvf7+nQoUMwL1asGMw3bNhAx0J9xVzS09Nhj50dO3bA/T/88EM61qpVq2CO+vqY8X5HrurU3Llz021Mnjx54LnNeoJ99dVXvud49tlnYc4qJcuWLet7Dr/YNbx169b0NX/++SfMhw4dCnNWJcXOBTP/39uYmBhYYVSnTh24/1133UXHqlChAswzMjJgfuTIEZi7KphjY2PpNr+eeeYZmLu+B6jnlxmvNmPVW6jPZCZU/XfgwAG6v/7iIyIiIoGhhY+IiIgEhhY+IiIiEhha+IiIiEhgaOEjIiIigeGrqisUCllEhHetxCpTXn/9dToW62XDepSw6pR77rmHzjFw4ECYs+qJQoUK2W233ebJWS8r1svJzGz16tUwZ/1PWrZsCXPWq8bMYF8xF3Z8zMqVK+k21gcpb968MGe9dVyVW3v27HG8O3/Gjx8Pc1fl4bJly2B+0003wbx58+Ywf/PNN+kcrsoDJDo6GlaCsOoQV48iVD1lxs/rq666CuYLFy6kc7BqLCYcDltaWponv/vuu+H+V199NR2LXZeeeOIJmI8aNQrmjz32GJ2ja9eudBuTlpZmBw8e9OSootTM7MEHH6RjsUq0AQMGwJxdf1x9mXr06EG3+cEqf1gvJzOzevXqwXzWrFkwZz2jSpUqReeoX78+3YacOXPGFi9enOX35Pr82DV85syZMF+yZAnMXcfQuHFjus2vdevWwdxVHcs+Q/Y7j1XHvfXWW3QO9Lm73pP+4iMiIiKBoYWPiIiIBIYWPiIiIhIYWviIiIhIYGjhIyIiIoGhhY+IiIgEhq9y9uPHj9vEiRM9+TvvvAP3X7RoER3rxRdfhDlrZJcrVy6Yf/fdd3QOVDLqkpKSAsvQR4wY4WscM7NPPvkE5qxpIytrvvXWW+kcRYsW9f2+/HA1gGzYsCHMWbPDunXrwnzz5s10jjZt2jjenT+seeqECRPoa1izPNYY9/3334c5K383MytYsCDd5gd77IHr3K1atSrMWUnwjBkzYN6hQwc6x48//ki3IVFRUVaiRAlPjpojm/Hzyszs66+/hnnhwoVhzh5t4HoEhN9SaDOzXbt2wfJ89vgPV6NXdg244YYbYL5gwQKYv/fee3QO1LQWPXLgUnbt2gXzP/74g76mXLlyMGePp2CPHnjttdfoHDVq1KDbkLi4OPid3rlzJ9yfNVo14+Xh7NrTtGlTmLNHrpjxR8ewcnIzs8TERBs5cqQn79y5M9y/YsWKdCz2WJKpU6fCnF3L/F5LXPQXHxEREQkMLXxEREQkMLTwERERkcDQwkdEREQCQwsfERERCYwQq+CAO4dCiWbGO8pdPsqFw+Ei/wx1fJcNeHxm//5j1PFdNv7t5+i//fjMdI5e7sfIj8/PwkdERETkcqb/6hIREZHA0MJHREREAkMLHxEREQkMXy0rEhISwqglwalTp+D+ycnJdKzDhw/DvFChQjB3PRLbrxUrViShm54SEhLC6BHpGRkZcJyUlBQ6x5YtW3y9p9KlS8O8QIECvsYxM/v777/h8RUoUCBcrFgxz/6Rkfg0OHPmDJ3j+PHjMD99+jTMY2JiYF69enXfc+zYsQMenxn/DFkrlL1799L52XnNWh5ERUXBvFSpUnQO9uj/tWvXwmMsWLBgGLUwyJcvHxwnKSmJzs2+g0WKwB8tPU/y589P52A/E/YdLFiwYBi1rMibNy8c5+TJk3RudnwMaw2RJ08e+prcuXPDnB2f2cVztHz58ll+XytXrqTb2HtjLT7YZ+U6R9HPfteuXZaUlBRC+7PjY9cGv9dKM369PHHiBMwrVapEx2LnNfsM8+TJE0Y/R/a9cbVOSk1NhXlsbCzMWQuP7MjJc5S1XDLjx8++O0zNmjV97e86R30tfMqWLWvz58/35LNmzYL7o30zvfXWWzBv1aoVzF09ufwKhULwbvVy5crZwoULPTm7iKxYsYLOceONN/p6T4888gjMb7nlFvqaUAh+pla1alV4fMWKFYP9pBISEuA4S5cupXNPmjQJ5nPnzoV5lSpVYL58+XI6B/vMu3btSqsNypUrZ4sXL/bk27dvh/sPGjSIzj9z5kyYt2vXDubsl8fw4cPpHOyiULJkSXiMxYsXtzFjxnjyJk2awHHQvplYjz3Ws4r1FWPfWbOL5xzCvoMlSpSwsWPHevJGjRrBcaZPn07nZr3T0tPTYf7UU0/BvFq1anQO1puOHZ+ZWfny5Z3n/T+xX4JmvN8a6jloZnbttdfCnPVzYq+pV68e3Z8dH7s2sL5iLux7y/o5TZ48mY7F/iHDPsP8+fPD/m19+/aF47zyyit07n379sH8mmuugfmoUaPoWH7l5Dn6/PPP023s3CpZsiR7XzD3837M3Oeo/qtLREREAkMLHxEREQkMLXxEREQkMLTwERERkcDwdXNzRESERUdHe/K4uDi4v+vGyokTJ8K8Z8+eMN+5cyfMDx06ROdwVbQgGRkZsPqH3dS5atUqOtbgwYNhzo77gw8+gLnrLn52YyMTFxdnN910kydn1RbspnUzflMeujHVzOzzzz+H+aJFi+gcd955J8y7du1KX5OcnGzz5s3z5OwGyilTptCx0Lluxm82ZTfBu25uRhVMLlFRUfA1rFjg2LFjdCx0LpjxmxHZe23fvj2dA30WLnnz5qU3MiMNGzak21hhQNu2bWE+fvx4mLdp04bO4fr55pRXX33V9zb22bKqp/j4eDoHOh9clUpmZqgjwPXXXw/3dd0YW7RoUZizG9dZlaarwo/d3MyULl3aXnvtNU/+xx9/wP1Z4YqZWfPmzWHObvxlBRdbt26lcwwcOJBu82vjxo0wP3LkCH0N+wyffPJJmKOf7aWg7yErYjDTX3xEREQkQLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwfFV17d+/31588UVPzqpA2F3uZmYdO3aEOavo+Pvvv2HuaumQHRcuXMjyvq5H2bPqgl27dsGcVY65+tjcfvvt/M35sGPHDpg//fTT9DWubciMGTNgziqnzMw2bNjga47M8a644oos78/aNpjxCgr2Wc2ePTvL82ZXRkYG7IH3+OOPw/1HjBhBx2rRogXMt23bBnPWM8rVT87Viw1JS0uDFTis9cUXX3xBx2KtRdjn+vLLL8O8R48edA7m4YcfptvOnTsHq2OuvPJKuH9iYiIdiz3Gf8CAATBH7VzM3O13nnnmGU82depUur8Zrupav3493Ldly5Z0HFb5w6qYWH8p1uvNzP91JleuXPAawH6nuao6WVWX34pEdu7mNFbRyqpKzcyeffZZmPvtO+b6rm/evNmTuSr59BcfERERCQwtfERERCQwtPARERGRwNDCR0RERAJDCx8REREJDC18REREJDB8lbOXKlUKlq6npaXB/Y8ePUrHYk3xWDNSVuqZk1JSUmz16tWePFeuXHD/unXr0rFY48ZevXrB3FWq99+2Z88emFeqVIm+hjUdZWW0HTp0gHmtWrXoHJGRvk5PMzPLnTu3lSlTJsv7u8ryWQPKBQsWwJw1FnRhTSOZmJgYu/rqq7O8/6OPPkq33X///TCfNm0azP/66y+YL126lM7RoEEDx7vzioqKoqXryGOPPUa3/f77777mfu6552D+/fff09c0a9bM1xxmZnny5IHXs0mTJsH92aMKzMwOHDgAc1Zuzh7f4Gr8mx0REd5/U7OG0rlz56bjLFmyxNe87PfH8ePH6WvWrVvna47z58/b9u3bPTm7XtavX9/X+GZmo0ePhnnx4sVhzs7d7Dp48CAskWcNZefOnUvHYs1p2bWhbNmyMO/evTudA12bJk+eTPfXX3xEREQkMLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwfJXN+G0gyBqwmfGmeB9++CHM3333XZifOXOGzjF27Fi6DcmfPz+9Ax1xVbOsXbsW5h9//DHMQ6EQzNesWUPncFVE+cEq0FweeughmLOqEVaJ5Gpke/DgQd/vKyUlxVatWuXJS5QoAfdnVRJm/BhZ1RhrkMg+czNeWcWcO3fONm3a5MldDXMZ1gDy7NmzMC9atCjMq1at6ntuv1iF6A8//EBfc++99/qagzUj/eqrr3yNcynp6el25MgRT86aDrOGx2b8nGOeeOIJmLsqBW+44QZfc6SlpcEKLtY8eNmyZXQs1OzUjF8v0XffzN2k1G+j6+joaGfF6z+1atWKbktPT/c1N6tOczVa9dso2Ozi9RJVcLEK7t27d/uegzXgZj+vqKgoOtbp06c9mavhuP7iIyIiIoGhhY+IiIgEhhY+IiIiEhha+IiIiEhgaOEjIiIigeGrqstvHx1XVRWruGCVNKy3V0JCAp3D753m4XDYUlNTPTnrF9O0aVNf45v5v8PeVbk1f/58X2MlJibayJEjPfkDDzzgaxyzi9VFyLPPPgvzvn37wpxVbbiwfmdmF3sERUdHe3JWvbVr1y46FquYGThwIMxnzZoFc9ZPKTvy5Mnjq4LLVe1RsGBBmLPKEdYPqG3btnQOV48kP1jfNFflFvvesnOOVffMnDmTznHzzTfTbUxkZCSskFu+fDncv169enSslStXwnzHjh0wZ9/1Pn360Dn+/PNPT4auk5mioqKc1ZL/lD9/froNVb+Z8QrDOnXqwNzVt6lKlSqOd/ffxfoR9u/fH+YpKSkwd1U356TXX38d5q5eYeh3jhnvk8iqTRs3bkzn6NixoydDfUUz6S8+IiIiEhha+IiIiEhgaOEjIiIigaGFj4iIiASGFj4iIiISGL6quhITE2HfIVa5wfojubBqBDaHq2qkXLlyvuYOhUKWO3duT856hEyaNImOtXr1api7qmyQL774gm7r3bu3r7GKFCkCqzqSk5Ph/t27d6dj5cuXD+YzZszw9Z5yumImT548virn5s2bR7eNGjUK5qwf0C+//AJz1N8uk99ePWa4Kon1LqpYsSIdZ+rUqTBPTEyE+fr162Huqp7IlSsXzB977DH6GoS910KFCtHXsIq9X3/9FeasQjQpKYnO8cEHH9BtzOnTp2GlFOttiHqzZXrllVdgznqYsQqqCRMm0DlQdSO6TmY6c+aMLV682JPXrl0b7u/qjzh69GiYt2jRAubff/89zDt37kznYBWDfrEq27fffpu+5rbbboM56+/Hflb169enc6C+adnFqrfYtcGM94fzUyFuxn9WZrgafN++fXR//cVHREREAkMLHxEREQkMLXxEREQkMLTwERERkcDQwkdEREQCQwsfERERCQxf5ez58uWzJk2aePKaNWvC/adNm0bHuvrqq2HOGkM2a9YM5qgsNJPf0uoLFy7YiRMnPPnp06fh/i+99BIdi5Vily5dGubPP/88zOvWrUvnyCmsND1Pnjz0Naxc9vz58zBnjSGfeuopOsfZs2fpNmbPnj2wZJ81ynM1PGVYw1zWwI+Vc5pdfL/Iq6++Sl/DSteRmJiYLO+bKSIC/3uodevWMK9atSodi5XGM0eOHLEPP/zQk7dr1w7uf9VVV9GxULNaM/7zY9/Nzz//nM7BsEa2ZhdLytH1bO7cuXD/rl270rEqVKgA84YNG8KcPRagcOHCdA7UADMjI4PunzdvXjg/e/yHq1ExOw5m8+bNMF+0aBF9Td68eX3N4XfuOXPm0Newz4M13x00aBDMjx49Sufw26w7O9gjIsx4A9ULFy7AvHLlyjDfunWrr/fEvk9m+ouPiIiIBIgWPiIiIhIYWviIiIhIYGjhIyIiIoGhhY+IiIgERsh1R71n51Ao0cz++7eI//eVC4fDRf4Z6vguG/D4zP79x6jju2z828/Rf/vxmekcvdyPkR+fn4WPiIiIyOVM/9UlIiIigaGFj4iIiASGFj4iIiISGL5aViQkJIRZSwkkPT2dbsuVKxfMd+zYAfNKlSpled5LWbFiRRK66YkdH3vktutR5wcPHoT58ePHYV6kCLwHi+Yu7PgKFiwYLl68uGf/5ORkOE7RokXpHKytAWtRkJqaCvNSpUrROY4dOwbznTt3wuMzM4uPjw+j1gO5c+em8zDbtm2D+cmTJ2Gek+1F/J6j2cE+96SkJJgnJCTAnLU8cXGdoyVKlPDsz9qXsPdkZrZx40aYs1YWFStWpGMx7H1t2LCBnqPsMzx16hQcKzY2ls6flpYG8+3bt8O8WrVqMGffTzP8Xd+/f78dP34c9v7we46y66sZ/66x62udOnVgfu7cOToHa+vi+g6WK1fOs7+fVjKXsmrVKpizVk8u7FrNjs/MrFChQvB7yM4Tdh6a8d8J7LuTU9fRXbt2WVJSEvxQfC18ypcvb8uXL8/y/keOHKHbChYsCHPWl4b1hnJhN25HRETAu9XZ8S1evBiO4+ojM2zYMJhPnjwZ5v3794f5fffdR+dgQqEQPL7ixYvbmDFjPDnrY4N6XmVii75PPvkE5qwn1fDhw+kc33zzDcy7d+9Oqw1Kly5tP//8sycvU6YMnYdp3749zKdPnw5zP9+NS2Gfod/voMv8+fNhPnr0aJj37dsX5k2bNqVzsH48kZGR8PhKlCgBe2OtX78ejnPPPffQudkFlPUC+u677+hYDHtfNWvWpOco+wx///13uP8111xD52cLgE6dOsF89uzZMN+7dy+dA/2joUuXLnR/v+cou76amc2cORPmQ4cOhfmSJUtgvmHDBjpHrVq1YM6+g+XKlYPzREb6+nXqVKBAAZiz3pSuudnCjh2f2cXv4YQJEzz5zp074f6HDx+m87M+ievWrYN5Tl3f6tWrR7fpv7pEREQkMLTwERERkcDQwkdEREQCQwsfERERCYwcuRuL3bXtqgpiN67efvvtvuZ+66236LbOnTv7GistLQ3epIXu4Ddz3wz59ddfw3zTpk0wZzcx797NnxruunkcCYVC8EbFwYMHw/1PnDjhHMuPTz/91Nf+ZmbdunWDeffu3elrIiMjLT4+3pPfeeedcP+XXnqJjsVuYr7jjjvoa/7/hlWmmZm1atUK5qwix+/3yYxXbzJ58+a1a6+91pOjzMxs4sSJdKyVK1fCvF+/fr7eE/vOmpnVqFHD11hmZikpKbBq58Ybb4T7X3nllb7fW8+ePWHObvJ13aD+2WefeTJWEWh2sZoXXZvy588P93cViXz77bcw//LLL2HObvItVKgQncOvjIwMS0lJ8eRxcXG+x3r44YdhzqrT2HXXdY66bo5nYmNjrXbt2p4cZWZmjRo1omOxm5jZjfmsGpPd8G1mVrJkSboN0V98REREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMP6rVV2uiosHH3wQ5n4reQ4cOEDnKFu2LN2GREVFWbFixTz5mjVr4P5PPPEEHYu1aEAVEmb8zntXNVSDBg3oNiQtLc327duX5XFYVZOZWZUqVWDOqhGyUwm1ZcsW36+JiIiA7TRYBV6TJk3oWFWrVoU5q0hkfdWefvppOsegQYPotpyA2j9kYo+yZ1UYrGKmT58+dI6XX36ZvzkgNTUVfnfY+cOuPWZmL774IsxRvzoz3v7CdXzZER0dDfuCsQpDV8UOg/rVmfFeS3PmzKFjoZ/Lxx9/TPePjIyEFb1Tp06F+3fs2JGO9d5778F84cKFMGftVu699146h18RERGw3xuroES/UzKx71qFChVgzlqLuPpG5iTWxsfVdgS1EDIzK1y4MMzZ99NV4eyX/uIjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGBo4SMiIiKBoYWPiIiIBIavcvbExEQbNWqUJ2cNNl1loKzx3ogRI2DOmgFeddVVdA5WKsicO3fONm/e7MlZYzYXVlaZlpYG89WrV8OcNTs181/OHhMT4+tYHn30UbptyJAhMO/VqxfMWYPCcDhM52Al89nBynUXLFhAX/PGG2/AfMqUKTBPSkqC+fjx4+kcfsvZMzIy7OzZs558xYoVcP8JEybQsVhjSla2zhokuhq9srJqJiUlBR5L3bp14f4REfzfbiVKlIA5a2jIHr/BHr2RXbly5YINF9l3ynUdve6662DOysDZsc+ePZvOgRqqombOmdh1lJWtu5p7ssdjLFmyBObsmsVKp83MGjduTLch586ds61bt3py9jvKNT56vIgZ/8yrV68O8wEDBtA53n//fbqNSU9Ph9cz9jvV9XulYMGCMI+KioL5J598AvP777+fzuGX/uIjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGBo4SMiIiKB4auqq0iRIrCCa8aMGXD/pUuX0rEGDhwIc9bQ7e+//4a5625ydOe9S548eWBjSlaNwJrumZnFxsbC/NixY77ek6v5m19paWmwqev8+fPh/qxKyYxXurA78v9X0tLS7ODBg568bdu2vsdyNaFFBg8eDPPhw4fT16D36hIREQGbi7IKLZfXX38d5uxnxao3WTWSGW8UyhQsWNA6derkyStVqgT3ZxV2Zv6rQFjD2l9++YW+hlUdZceyZctgXr9+ffqacePGwZw1emzWrBnMWUNeM7NWrVp5Mtao14xfR48ePQr3d1X+rVy50lfOZGRk0G2uRtdITEwMrOBiFWWLFi2iY7Emvq+88grMH3/8cfqeclI4HLbz5897clYt6Go0yxqM58qVC+Y7duyAef/+/ekcrupgRH/xERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwPBV1cX47XVixntWPfXUUzBnvUhcfUgSExN9v68LFy54suuvvx7u+3//9390nDFjxsB8+vTpMGf9TFhPGjOzWbNm0W1Ivnz5YOUK66Plqrbo0qULzEeOHAlzVmXi8tVXX/l+TVRUFOzR9Oeff8L9XdUQDzzwAMy3b98O88mTJ8Oc9fwyM/vxxx/pNj9YVQPrr2XGq1D2798P81q1asG8cuXKdA7UV+xS0LGwvls9evSg47DqkC+//BLmw4YNg3lOVm651KtXD+anT5+mr2Hf3RtvvBHmu3fvhjnrAZUdqamptmfPHk9etmxZuP93331Hx7rjjjtgnjt3bpizc5FV2Zr5vzadOHECVvSyPpPvvvsuHev555/3NTfqgWbGq8DM3NcfJioqykqVKuXJ165dC/c/c+YMHYudi6za7dlnn4W5q4J77ty5nsz1vdFffERERCQwtPARERGRwNDCR0RERAJDCx8REREJDC18REREJDBypKqLVSQdP36cvmbLli0wv/XWW2HeunVr3++rSJEivvY/e/Ys7AnG+oqxO9zNzKZNmwZzViGWnZ5c7G555tixY7DHTpUqVeD+rj5I7PNjPXSyUzXCKjey49prr/X9ml69esG8X79+MGe921gln9nFCpj/pk2bNtFtEyZMgPnQoUNhfurUKZjv3LmTzuGqrGBQJRrr88R6eJmZffHFFzBnva9YhR+rnMppr732GswbNmzoeyxWEcmqYFetWkXHQttc1/bcuXPTCi7EVRHEzl9Wrcgqf1jFnJlZ0aJFHe/OKyUlxVasWOHJWb+qefPm0bG+/fZbmKPxzfjPytUrK2/evDB/8skn6WsOHDgA++zdfffdcH/2/TQzWOHnwqorXQ4dOuTJ8uTJQ/fXX3xEREQkMLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwMiRcvZffvkF5jfddBN9TYMGDWB++PBhmLOy33379tE51q1bR7ch6enpduzYsSzvz5o2mpkVKlQI5idOnID5Rx99BHPW+NLMrGXLlo535xUfH2/dunXz9RqGlYfWz1kkJgAAIABJREFUrVsX5suWLYP5hg0b6BzZKePNSayklH3uHTp0gPn8+fPpHO3atYP5ww8/fIl3lzVVq1al21yNG5H33nsP5qixbyZXSSly9uxZW79+vSevUaMG3N/V4JIdO2t43LdvX5iza1VO6927N8xZg1Yz/sgHVsLMrieukmP0eANWeu/CHm3gKo1nv1tQqbUZv/4sXLiQzuEqBUdKlixpL7/8cpb3R42hMw0fPhzm58+fh3nnzp1hzn7fmLnPH6ZkyZI2ZMgQT84eaREXF0fHYg3J/fwMLwU1VmbzmukvPiIiIhIgWviIiIhIYGjhIyIiIoGhhY+IiIgEhhY+IiIiEhihcDic9Z1DoUQz2/3fezv/M+XC4bCng6mO77IBj8/s33+MOr7Lxr/9HP23H5+ZztHL/Rj58flZ+IiIiIhczvRfXSIiIhIYWviIiIhIYGjhIyIiIoHhq2VFQkJCuHz58p6cPRqatWcwM0tJSYE5e9R6vnz5YO73kfhmZitWrEhCNz0VLlw4XKZMGc/+oVAIjpOYmEjnYC02XK9B2CPYXdjx5c2bNxwfH+/Zv1ixYmwcOkf16tVhjh4dbmZWuXJlmLNHs5uZRUdHs/cFj8+Mn6Pbtm2DY7ketX7y5EmYs8/23LlzME9ISKBzlCtXDuZ+z9Hk5GQ4zvbt2+nc1apVgzk7DtZyoGDBgnQOto0dH/v8GNc5yn7u7Jrh99pziffl+xxln+GWLVvoPKyVB+P3nDYzK1WqlCfbtWuXJSUlwQtjwYIFwyVLlvTkMTExcPyVK1fSuaOiomAeGYl/dZ09exbmFStWpHOwth+bNm3KkXOUXXvM+OfBzlHWhoX9PMzMMjIyYL5q1Sp6jsbExIQLFCjgyUuXLg3HcrUdYW2l2DnHrvt+z3XXOepr4VO+fHlbvny5J2e/7H788Uc61urVq2F+7bXXwvy6666DObt4u4RCIXi3epkyZez333/35Lly5YLjfPrpp3QO9mGznlzM0qVL6baICPwHO3Z88fHx9sgjj3jyxx57jI1D5/7mm29g/sILL8B86tSpMN+xYwedg12s2PGZ8XP01ltvhfu3bt2azj9jxgyY79y5E+abNm2CeadOnegco0aNgrnrHJ0zZ44nZ/3AWP8wM7OxY8fCfPPmzTCfO3cuzF29jtixs+Njnx/jOkfZ3FdeeSXM2bWnUaNGvufPzjnK+kndcMMNdP6ffvqJbkPYOX3gwAH6mmHDhnky1qvP7GKfpy+//NKT16xZE+7v+sdr0aJFYV6kCPx9TX+vvPrqq3QO9o+Phg0b5sg52r59e7pt+vTpMK9UqRLMf/vtN5izn5MZ/wdLXFwcPUcLFChgvXr18uRvvPEG3H/ixIl0/ieffBLm7DrKFpV+fuZm7nNU/9UlIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGD4urmZQXf9m7lvPH7wwQdhvns3vt+KVWhk5+ZmJjIyEs7DqjrOnDlDx+rTpw/M2U1os2bNgjm7gTk74uPjrWvXrp58zJgxvsdiN4KOGDEC5j179oT5+PHjfc+dHe+99x7MXdUe48aNgzm7IRpVspiZffLJJ5d4d1kXEREBbwb99ttv4f5XXXUVHatx48a+5mY38rpuHPUrJSUF3qCanUoPVpTw7LPPwpxVBLmebs8qZrKD/XxdlY8VKlTwNUeLFi1gzm5cNzObPXu2J2M3zJqZXbhwwU6dOuXJ2WfoMnToUJizG10HDRoE84MHD9I5unTp4us9nT9/HlZqJSUlwf3Ztc+M/75bt24dzNl1l90obGaWP39+uo1JSUmBP+OjR4/C/V0/w5dffhnmderUgXnbtm2z8A7/01tvveXJDh8+TPfXX3xEREQkMLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwfFV1paWlOR9t/k/sDnsXVA1gZvbZZ5/BvEGDBnSsEiVK+J4fYS0dWMWBmdnPP/8Mc3anuat1A/Phhx/62j89PR32VOnbty/c/95776VjtWnTBub333+/rzynJSYm2siRIz25q2qFadeuHcznzZsH886dO8Pc1XLAr4iICIuNjfXkEyZMgPsXKlSIjsXaWbA+bMOHD8/CO/xP7BH7TGxsrNWuXduTr1mzBu5fpUoVOtb69eth/uuvv8K8Vq1aMJ8yZQqdA/VNu5S0tDQ7dOiQJ2c9nVgvPTN+PUGtacx4vyzW8sTMrGXLlp7MVSmUP39+eM6z1ibsWmLG+6eh77gL+nln8vM7zexitSDqY8X6Efbv35+Oxaq32O8Dv1V8Zv6/g2ZmxYsXtyeeeMKTu1rEMM8995yv/SdPngzz2267jb7m4Ycf9mSsrZKZ/uIjIiIiAaKFj4iIiASGFj4iIiISGFr4iIiISGBo4SMiIiKBoYWPiIiIBIavcvaoqCjYiJE1SGMlqC6LFy+GeWJiIsw3btxIx/Jbzp6YmGgff/yxJ0dN+szMSpcuTcdijSxZOeDatWuz8A7/00MPPQTzAQMG0Ne4Gi7+U9WqVem2559/Hub79++HOWtkm9MKFy5svXv39uSsJJiVTpqZDRkyBOYfffQRzFEZtpnZqlWr6By//PIL3eYHG+fEiRP0Naysm5Xfv/322zBnj3sw498Dv1g58vTp0+lrWFPMN954A+askW2nTp3oHKwc2SUqKsqKFy/uyVnpdnaaezLZeSSBX/v27bPBgwd78h9//NH3WN27d4d5w4YNYb5kyRKYu657f/31l6/3dOTIEXgN6NevH9y/Zs2adCzWgJb9zmGPHnGVbt988810GxMbG2v16tXz5Oz6zh4FYcYbbbOG3ey7PnHiRDrHHXfc4clcpff6i4+IiIgEhhY+IiIiEhha+IiIiEhgaOEjIiIigaGFj4iIiASGr6ouhjVOc1WULF++HOaLFi2CeZEiRWC+bNkyOsemTZvoNiQuLs5atWrlye+66y64P2r4mWn06NG+5v5fiImJgRUGrMpl8+bNdKxbbrkF5kuXLoU5q8pjn6uZ2dmzZ+k2JiIiAlbHsAZ3t99+Ox2LHeP3338P89WrV2fhHf4n1tjQr+bNm8N85syZ9DU33XQTzFlV13333ef/jfkUDoctNTXVk7NGlqySzow3MJ01axbM9+zZA/OKFSvSOVwVO8yZM2fgdYs1uXVVs7BGyStXroQ5q4Jj31szg9fE5ORkun/p0qXtzTff9OQ1atSA+1933XV0LPb9+Pbbb2Hup2o1U7NmzXztX7RoUVg5W7hwYbh/pUqV6Fjjx4+HOWsQzX7f9ezZk87BKnBdIiMjLSEhwZOjzIxXGJvx6warumZNXVHFdaZ9+/Z5MnQdyaS/+IiIiEhgaOEjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGD4qurKyMiw06dPe/L8+fPD/VlfDzOzli1b+srZnemoJ0ymr776im5DcuXKZYUKFfLkcXFxcH+Wm+HeIWZmr7zyCsxdd/7nlLNnz8KeYKhqw8zsiSeeoGOxir1GjRrBnPXEeuCBB+gc2alGOH78OKyCYZ8Hq9Ay473mWCXY559/fuk36GN+P2JiYmDOKrfMzMqWLQvzvXv3wvzWW2+FuatfVp48eeg2JCkpCf4cWWUI681kdrF6CmGVWKxPYIsWLegcrN+ZS968ea1+/fqenFVRvvDCC3Sso0ePwpxde5OSkmDOqsOYfPny+drfzGAPPTOz3bt309d89tlnvuZ49NFHYT5ixAhf47gcPnwY9q1j1/ann36ajtW1a1eYs+vls88+C/NPP/2UztGkSROYf/jhh/Q1qampsMqRXTNYFZqZWdu2bWF+7bXXwjw7velQ38zcuXPT/fUXHxEREQkMLXxEREQkMLTwERERkcDQwkdEREQCQwsfERERCQxfVV2hUAhWj7DeN3Xq1KFjoeowM37XODNy5Ei6bfv27b7GSk9Ph1UPrAcLqyAwM3v33XdhPmjQIJizKowyZcrQOS5cuEC3IaFQyCIjvR85q55ilVBm/P2y/misN5urD9GcOXPoNqZQoULwfbPeRayfkxnvA8X6i33zzTdZeIf/6ZlnnoE5q97IqfHNePUWq4B55JFHYP7BBx/QOVBPI5ciRYrACq4dO3bA/dPS0uhYY8eOhfmxY8dg3qFDB5i7qo5YDzEX1o+satWqcH9Xj6Lhw4fDHH3PzXhvKHa9MsM9zNi548L6aG3cuJG+ZuHChTBnPehc5zvz559/+tq/VKlS9OeOsN91Zvwz/+mnn2DOKhJd157snKOhUMhXdVVKSgrdxnqxscrABQsWwJxdA8zw72jX70f9xUdEREQCQwsfERERCQwtfERERCQwtPARERGRwNDCR0RERAJDCx8REREJDN/l7KhMkjW57Ny5Mx1rypQpMGclxDfffDPMXeWszZo1o9uQXLlywYarrHnhX3/95Wt8M7Nq1arBnDWle+qpp3zPweTJk8eqV6/uyYcNGwb3r1WrFh2rRIkSMG/YsCHMWXmtS3p6uu/XpKam2r59+zw5e7QC+zzMzIoXLw5z1vSPlUPnpHPnzsFmljt37oT7s3PXzCw+Ph7md999N8xZE81evXrROZYtW0a3+cHKZV0NPNk15o8//oA5a2pYrlw5Ogcrq3YJhULOBor/5CodR+e6GS8dZ9g5zbiufRkZGfDzYo+UcDX3ZY8eYMd38OBBmJ89e5bO0bx5c7qNjbVu3TpPfuTIEbi/6/Njj0RhTaDZz6pbt250DvTohEtJT0+3xMRET84+j9dee42OVaNGDZizc4iVs1esWJHOgeTKlYtu0198REREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMEJ+7v4PhUKJZsY79l0+yoXDYU+nSR3fZQMen9m//xh1fJeNf/s5+m8/PjOdo5f7MfLj81v2KCIiInK50n91iYiISGBo4SMiIiKBoYWPiIiIBIavPgIJCQnh8uXLZ3n/M2fO0G1Hjx6FOXpMtpnZFVdcAXPX47gTEhJgvmLFiiR00xM7vuTkZDiO65HYJ0+ehPn+/fthHhcXB3N23C5+j+/cuXNwnOjoaDrH+vXrYc4+D9Qqw+zi4+2ZUCgE840bN8LjMzMrWLBguGTJkp6ctcxwtTyJiMD/LmCvyZs3L8xd58n58+dhvn79evoZli1bNsvv1WXVqlUwZ59J3bp1fc/Bxlq1apWvc5Tdi8jOETOzbdu2+XpPrDWF63vAsO+gmf/rKLtWmpkdPnwY5gUKFIA5a8PiOkeRXbt2WVJSEvzh+z0+l02bNsG8YMGCMGfHlx1+r6PZgVpfmPHzvWjRojDPznFn5xw9ffo0HMt1rzBrv8G+V+wYXd919L4OHTpkJ0+ehC/ytfApX768LV++PMv7L1myhG774osvYP7xxx/D/IMPPoA5W0iY8Z5DoVAI3q3Ojo/1FGG9jszMpk+fDvOnn34a5o0bN4Z5NnsB+Tq+LVu2wHFcvVHYgmzXrl0w/+6772Du6qHDFit16tSh1QYlS5a08ePHe/JixYrB/VlvH7OLvc38vIb1KWOLWjOz7du3w7xy5crwGMuWLWvz5s3z5GzR5cLeF7u4+fnuX2qsuLg4X+coWyC6FiW33HILzNk5N3r0aJi7vgcXLlyAeWRkJD1H/V5Hv/zyS7rtrbfegnnbtm1hzq4/bKHE1KtXj27ze3wujRo1gjnrAzlo0CCY+13Ymfm/jmZHpUqVYM7O0Yceegjm2enpyI7PjB/j3Llz4f7s+2nGfxeyY3/wwQdh7upvh/rv9evXj+6v/+oSERGRwNDCR0RERAJDCx8REREJDC18REREJDB83dycnJwMb6xkFT41a9akY7GbmN9++22Yt2nTJgvv8D+5blxl+w8fPtyTP/PMM3D/DRs20LHYTYRXXXUVzLNzE/OOHTt8vwbZuHEjzO+55x76Glax16dPH5hXq1YN5q6bmydOnEi3MbGxsb6qj0qXLk23rVmzBuYDBw6EOatAmTZtGp2jVatWjnfnFRERQW+6RmJiYui2bt26+Zr70KFDMHfddOgqAEDOnz8Pq7G2bt0K93cVN/z8888w/+2332DObjR33dzsqrhiTp8+DW8Sbd68OdyfFQyYme3duxfmrFiCXTNGjRpF52DXaiYlJcVWrFjhydnPynVtHzlyJMz79+/v6z2tXLmSbmPVjUx6erodO3bMk7Nz3VWZyz4PdpN2dm5izo60tDQ7cOCAJ7/uuuvg/pMmTaJjffTRRzDv2LEjzB9++GGYL126lM5x9dVXe7LY2Fi6v/7iIyIiIoGhhY+IiIgEhhY+IiIiEhha+IiIiEhgaOEjIiIigeGrqisiIgI+Gp/dYc8eN+6CHj1tZnb77bfDnPX2MnPf1Y2UKFGCVnAhrP+UyyeffOJr///7v/+j2z7//HNfYx09ehS2c+jZsyfcn911b3bxkeYI6/vFeni5KtMaNGhAtzHnz5+H1Tn79u2D+//00090rHfeeQfmrCqIufnmm+k2V/8ZJD09Hfa++eabb+D+7PMwMxs3bhzMWXsRVl3EWnVkR3R0tFWuXNmT796Nn67PPlcz3gepRo0avt4Tq3o0M/v+++99jWVmlj9/fmvWrJknX7hwIdx/6tSpdCxWEXXrrbf6ek9XXnkl3Ya+T64WBRcuXIDnaOvWreH+RYrAdlFmxtsa+OXq6ciqV/v27QvzlJQUWCVWoUIFuD+rhjTjPcdY9davv/5Kx2LKlCnj+zXp6emWlJTkyVEfRDN+zTDjvbemTJkCc3admTNnDp0DtVBxtSnRX3xEREQkMLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwPBVzh4bG2t16tTJ8v6u5m+ffvopzO+77z4/b8lZVum3QaJfrBzPpUmTJjBftmwZzF0l667Ggki+fPng/CNGjPA1jpnZtddeC/MJEyb4GqdUqVJ0m6sElYmOjoYlsKws9v3336djsWZ5rOHq7NmzYZ6RkUHn8NukNDIy0goXLuzJ2c8RlXlmWr58OcxZg0tXQ9f/tlOnTsF8yJAh9DXt2rWDOTtuVtLtKvV+8cUXYf7SSy/R15jhUlt2bYiLi6Pj7NmzB+aDBw+G+Ztvvglz1pDXzKx9+/Z0G5I/f35r2bJllvd3PZKElcD/+eefMGcNQVevXk3n8Ps4BnaNiYqKgvsnJyfTsXr37g1zVuJfrFgxmNeuXZvOMWvWLLqNiYmJ8fXYB9djQdj1kmGPSrn//vvpayIi/P0NR3/xERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwPBV1ZWcnGx//fWXJ0cN98zcFVf9+vWDOav2WrFiBczZXfxmBpusuZw7d842b97sydPS0uD+8+bN8zW+mf+mlN9++y3dxu7wZ6Kjo2EjvW7dusH9Bw0aRMdiTel69OgB86pVq8Lc9fPwe6d+dvz888++XzNp0iSYV6xYEeboO5Nd58+ft23btnly1EjSjFf9mPFqi7Vr18I8PT0d5sePH6dzXHPNNf9Pe3cep1Pd/w/8fWWYhTEmY8/MWFOWkhQqQrY2qSy3LSlSt4oWlW6ELKEosnS3S+4sLSpRtkrWVKKsSci+DGMMs7i+f/jNH9/O6/VpznXP7/t4cF7PP1/nc53PdeY615mPcd7nTbf5MXv2bJinpKTQ17Amt8nJyTC/9957YT5gwAA6B/u5R4I1oPz111/pa1hFFGu2zI7lmWeeoXOga0Z0dDQd71f9+vV9vwY1yzYz2DzUjDcDjQS7jkaCVRiyhpzsd5FLnTp1fL/GzN/1t2nTpnQba5jLrv2DBg2C+bBhw/L9fv6O/uIjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGBo4SMiIiKB4auqq1ixYrSCC3H1D8nMzIQ5uyuf9X5h/ZFc+2JYH6SEhAQ4ftKkSb72b2bWsGFDmG/evBnmrsoxP/1wzM5VoNx1112enPVmigSrBNu2bZuv3Iz3vonEZ599BnNXL6sdO3bA/NNPP4X5008/DXPWH8nM/R1BTp48acuXL/fkTz31FBzfpk0bui9W0cb6ILHeV66qI1Ql6XL48GF76623PPmECRPgeFdl4xtvvAHz6667Duavv/46zC+//HI6x86dO+k2v1q1agXzm266ib5m5syZMPfbX8t1Xc/NzfVkp0+fpuOzsrLsjz/+8OSsAq9q1ap0X36rYGvXrg1zV4/JDh06+JqDOXjwIMxr1qxJX8P6wKHrtBn/uU+ZMoXO0aNHD7rNr3A4DHP2+9zMrH///r7mGD58uO85XNdYRH/xERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwPBV1cXs378f5q4+U6xPUJMmTWDOepc8/PDDdI6JEyfSbUhUVJQlJSV5cta7KCsri+6L9f1ZuXIlzOfNmwfzli1b0jn8VpVVqVLF5s6d68lZxVMkWJUWq9xw3fHP+oFF4tZbb4V5uXLl6GtYxRfrr9OzZ0+Ys6pAs3OfiR8lS5aEVRr33HMPHO+qhLj55pth7reShn1nzcymT5/ua19JSUnwu7Nx40Y4nvX1MTO77777YL5s2TKYs75is2bNonMUZFUXE0mfKXYussqqZ599lu5r/fr1niwmJoaOP3v2rLNP41+5qgJLly4N8wMHDsD8hRdegDmruDQze/vtt/mbA8LhsLOq7a9++eUXuo19P9PS0mDevXt3mLNKUzP/FX4uf/75J8z79OlDX7Nq1SqY33///TBftGgRzMeNG0fnQL3Cjh8/TsfrLz4iIiISGFr4iIiISGBo4SMiIiKBoYWPiIiIBIYWPiIiIhIYWviIiIhIYPgqZ8/MzLQNGzZ48iNHjsDxRYsWpftijci+++47mP/zn/+EuauB38cff0y3+cHKvevUqUNfw0oIWQNI1kySNb4rSKzUmzWkM+MlzyNGjIA5K5dlc5uZnThxgm7za9euXTD//fff6WsaNGgA8969e/uae/To0XRb69atfe2LYZ9HXFwcfc2LL74Ic1fjVsT12IqoqAJ5YgYtHx42bBh9zZo1a2B+4403wjw+Ph7mrtLs1NRUus0vVtY9efJk3/OzprUMK/GPRG5urh09etST+y1rNuOPEvD7yAXU+DZS6enp9s0333hy9ugR1zV89uzZMM/IyIA5K42/6CL+NwzUePvvZGZmwkdIsO8ze5yGmVlsbCzMO3bsCPN+/frB3NXQGT32wNXkWn/xERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwAi5Knc8g0OhQ2b2x/+/t/N/JiUcDpf6a6jjO2/A4zO78I9Rx3feuNDP0Qv9+Mx0jp7vx8iPz8/CR0REROR8pv/qEhERkcDQwkdEREQCQwsfERERCQxfz5NPSkoK+3lEu6sdQHR0NMzT0tJgnpmZCfMiRYrQOWrVqgXzH3744TC66Sk2NjackJDgGY8yM/6IezOz48ePw3z79u0wr169uu85mHXr1sHjS0pKCqekpHjG+338u5nBR9Kb8c+8VCl4j5klJyf7npsdn1nBHuOpU6dgzj7bffv2wbxmzZp0juzsbJhv2bKFfoboO7h37164nxIlStC5N23aBHP2qHf2XsuUKUPnYC0zfv/9d3h8iYmJ4fLly3vGs3sR2WdkxlvpnDx5kr4GQe8nD3pUvpnZTz/95DxH/VxHc3Nz6TZ2PWHHWK9evXzPmwe1jjlw4IAdP34cfqnY8bHWH1lZWXTu3bt3w5z9PmCuuuoquo3ta9OmTfAzjI+PDyclJXnGs9YMrrYx7Pddeno6zFlrCnYemvHvs+s6mpiYGK5QoYInZ9dR9vvczOzQoUMwZ22E2DWrSpUqdA50vu/fv9/S0tLgG/a18ElNTbXvv/8+3+O7d+9Ot7GDmDt3LsxRjzAzs3LlytE5WN+v2NhYeLd6QkKCdevWzZOzflJNmjShc7P+XqyH19SpU2HetGlTOgcTCoXg8aWkpNiKFSs8ueukZd5//32Yd+nSBeYdOnSA+aRJk3zPzY7P7Nwxos89JibG9zw//vgjzD///HOYP//88zD/5JNP6Bx//vknzBs3bgyPkX0HBw0aBPfTtm1bOvc111wDc3YRZe+VfeZmZnXr1oV5t27d4PGVL1/ePvjgA0/OFl2u69F7770Hc9RnyeWBBx6g2x599FGYlyhRgp6jfq+jx44do9vuvPNOmLPeW37mzfPll196sr59+9Lx7PjYIo39AjQze/zxx2H+008/0dcgq1evpttQTyozs7p168LPMCkpyYYMGeLJ2T+0Xb3vWD/JpUuXwpwtoh555BE6B/sd6bqOVqhQAfYRY9fRSpUq0fmnTJkC84ceegjmzZo1gzlbG5iZLV++3JO5esDpv7pEREQkMLTwERERkcDQwkdEREQCQwsfERERCQxfNzfv3r3b+vfv78nHjx8Px7MbG83MihUrBnN2M9uECRNg3rNnTzqH3xtaL7nkEhs7dqwnnzVrFhzfvHlzuq8lS5bAnN2V36ZNG5ifPn2azhEJNr9fnTt3hjm6MdXMbNu2bTAfNmwYnWPw4MG+31coFIKfO6scOXv2LN0Xq1C74447YP7qq6/CvHLlynQO1zbk2LFj8CY/9r1xFRi0atUK5o0aNYI5+zwOHz5M5+jatSvMURGB2bnKGHaTKDJ69Gi6jVV8su/zuHHjYD5q1Cg6RyTnKINuIjbjn5OZWdWqVWHOKnlYVY7rCf4tW7b0ZMWLF6fjz5w5A7/vb731Fhzv+gxZ0YfrhnPEdR3ds2ePr33FxcXBG5bZecsqWs3M6tSpA/OJEyfCnFWIuop8XDc+M2lpaTZv3jxP/tRTT8Hx7EZlM14kwm5i/vDDD/PxDv83dM13/a7TX3xEREQkMLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwfFV1VaxYkVZwIZ06daJZCGl1AAAgAElEQVTbFi1aBPPffvsN5g0bNoR5u3bt6BzsUdlMRkaGrVq1Kt/vacCAAXRfrOopIyMD5l9//TXM2WPezXhFBxMKhWC1x9atW+F41j/MjPe3ef3112H+9NNPwzySR+hHwtXTjWHtABjWv+yPP+iT4Q31FXMJhUIWFeX92rL+Nqzay4y3XBk4cCDMExMTYc4qU8x4O4CC4qomufzyy2HOWouwvknsuxypzMxMW79+vSdn1T/s+2lmVq1aNZiz98z6ybmg77qrGjI6Ohq+r5EjR8LxLHdhvchYBR6rIjbjLYmYiy66yFfFMOtV5cJacrRv3x7mrvZJkShbtiys4Jo/fz4c/+uvv9J9oXYSZv77xrkqD1GVnatHmv7iIyIiIoGhhY+IiIgEhhY+IiIiEhha+IiIiEhgaOEjIiIigaGFj4iIiASGr3J25sSJEzCfPXs2fc1LL70E87vuugvm8fHxMHeV17PSP6Zo0aLWoEEDT37gwAE4vkePHnRf69atg3mFChVgzpoKsp+TmdnOnTvpNuTkyZO2YsUKT87KsF3l+qdOnYL5V199BfOFCxfCvFKlSnSOmTNn0m1Mdna27d2715OzklJWfm9mNmnSJJi///77MGeNG10l6+znyJQoUcLatm3rybOzs+H4yZMn032xEtjdu3fD/NixYzBHP+88fhqOmp37efzwww+efMeOHXA8GpuHPUKhZMmSMGePHXjjjTfoHJGIjY21K664It/j2ffT5YYbboA5a/rpeuwA+gwjaXbMmpFu2rSJvmbNmjUw37x5s685nnzySTqHq9QdiY6O9v0oEWbo0KEwHzJkCMwXLFgAc9cjFy655BL/b4xITU2FOfv9bGa2YcMGmP/8888wX7x4McxnzJhB56hfv74nczWm1V98REREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMHxVdaWnp8NmmqhSyOzc3e8Mq6BgVUwvvvgizCtWrEjnYJUufqEqGjNeIWHGq7euvPJKmLOmdE888QSdw1U1hxQrVswaNWrkyVnjudWrV9N97d+/H+asMW2rVq1g/sILL9A5WFWZq4KhcOHCVr58eU/OKvNY5ZYZr3pi85ctWxbmrMLPzKxMmTJ0mx/Lli2DuavqiVWnvffeezDPysqCOWvuacavDUxcXJxdddVVnnzcuHFwvKvyb8KECTDv168fzFlT2sGDB9M5lixZQrcxZ8+ehU027733Xjh+zpw5vudg194zZ87A/Nlnn6X7evnllz0ZOxfy5kCNnVkz0GeeeYbuyy/03TczeE7ladGiBcyfe+45mOfm5trx48c9+fTp0+F41/Gxiis2d7ly5WDuqqpyNbllcnNzYbU2e7+u31MdOnSAOWs62rx5c5iz77MZrtrNycmh4/UXHxEREQkMLXxEREQkMLTwERERkcDQwkdEREQCQwsfERERCQxfVV1RUVGwz00kd+U//vjjMEdVY2YGqwTMzG677TY6R0xMjO/3hbB+Ma5qjz179sD87NmzMJ82bRrMExIS/ubd/fdq1qwJ83379vneF+uPUqVKFZizO/sLWkZGhu/5+/fvD3NWqcR+Xqwi0YxXDPrF+uV99NFH9DUtW7aEOaswZP3kSpUqRedgfXr8GjNmDMxZPy4zs3nz5vmaY8SIETBnlTRmZm+++aavOczO9blC/aFYlWYoFKL7Qj2KzMy2b98O86ZNm8L8gQceoHMUKlSIbkNycnJglQ3qg2jm/g6y62KfPn1gfvXVV8O8oKonzc79PNB1uW/fvnC86/vBKkfbtWsHc1adyiqhzMwyMzPpNqZQoUK09yBSpEgRum3btm2+5maf4aOPPkpfc/DgQU/m+v2vv/iIiIhIYGjhIyIiIoGhhY+IiIgEhhY+IiIiEhha+IiIiEhg+Krqio2NtVq1auV7fO/evX2/ocaNG/vKly5dSveF+uG4ZGZm2saNGz35Nddc42s/ZmaDBg2Ceffu3WEeyc/KL9ZDh1VcLV++nO7r6NGjMB86dCjMWYXA+PHj6Rzos4jUjh07YI76EOVhlVKsJxerPGQVjAWJ9SJatWoVfQ2rQqtUqZKvuVn1m5nZqFGjfO2L2b17N8wTExPpa9h3MDk5GeY1atSAuavfWc+ePWF+33330df4dezYMbqNzbN27VqYf/HFFzB3Vd6gfoiuKp6iRYvCCq7c3Fw43lV9x76f7LrBKi67dOlC52A96wpK+/bt6bZdu3bBnPVa++STT2DuOkc2b97seHcFw1W5xrDeeHPnzoU56+9pZpaSkuLJoqL48kZ/8REREZHA0MJHREREAkMLHxEREQkMLXxEREQkMLTwERERkcDQwkdEREQCw1c5e3Z2tu3fv9+To4Z7ZmbHjx+n+5o5cybM09LSYI6a3pnxpntmvOEpw5qwTpo0CY6/6CK+bty5cyfMx40bB/N3330X5qz83fUaJjo6Gpaus0aS7BjMzObMmQNzVvrLyqqvvPJKOgcrJ3cJh8OWk5PjyVm5d4cOHei+Lr30UpgPHDgQ5qdOnYK56+eYmppKtyFHjhyx6dOne3L2HXQ1uWVN//w0JzRzP5LAr+zsbNu7d68nb9iwIRzPyrPNzKpWrQpzv00T2bkTqZycHNhUsUSJEnD8gAED6L4+/PBDmKOfoZnZjz/+CPO6devSOZYtW+bJ0tPT6fhwOGzZ2dmenD0ew9UMuXLlyjDv168fzL/99luYu64lrNFrQenVqxfdxh4Pw3531a5dG+aucnb23YnEK6+8AvNHHnnE975Y2To7H1DJeh60bmCPTzDTX3xEREQkQLTwERERkcDQwkdEREQCQwsfERERCQwtfERERCQwQuFwOP+DQ6FDZsY7hZ0/UsLhsKermo7vvAGPz+zCP0Yd33njQj9HL/TjM9M5er4fIz8+PwsfERERkfOZ/qtLREREAkMLHxEREQkMLXxEREQkMHy1rEhKSgr7ecT+unXr6LbExESYs0fvly5dGuaohUaeMmXKwPyHH344jG56iomJCcfHx3vGs8f+HzlyhM4dExMDc1cbD6RSpUp0W5EiRWD+008/wePz+/nt2LGDbmOPA2ePFWfvNRLr1q2Dx2fm/xhdj8tnMjMzYc5aDhQtWpTuKzo6GubsGP0eH2ujYcaPg7XYYO1FChUqlO/3k4cdX8mSJcPJycn5niMjI4POsWfPHpifPHkS5uwaU7ZsWTpHKBSC+fr1632fo+xaxq6VZmbbt2+HOWoZYcaPsXz58nQOZOfOnXb48GF48OwzZO/J9R08evQozAsXLgzzuLg4mLuOj13Ltm7dCj/DhISEMPo5xsbGwv2w883sXHsP5PTp0zBPSkqCuas9A/uZuK6jsbGx8Hch+lzNeIsUM36M7HyvV68e3ReDjn/Xrl125MgReI76Wvikpqba999/n+/x7KJgZtayZUuYs74irK/QCy+8QOdgr4mNjYV3q8fHx1u7du08+S233AL38/bbb9O5a9SoAfP58+fDnPX9cs3BFhmJiYnw+Px+fp06daLbWO+bqVOnwpx9YSIRCoVotYHfYxw2bBjdFhWFvx6s31Hbtm1h3qhRIzoH60XEjtHv8bHeaWa8R1uPHj1gvmTJEpi7fjEz7PiSk5NhnyLWP2zlypV0jqeffhrm33zzDcw7duzoaz9mfEFfqlQp3+fo6NGj4XhXP7nbb78d5n/++SfMe/fuDfPnnnuOzoFcffXVdFtycjI8V9gvuhEjRtB9zZgxA+ZsAcDel+t7zvpcNWvWDH6GpUuXtpdfftmTsz5a3333HZ2bLXC2bNkCc/b5uf5Bzf7B4rqOxsfH29133+3JJ0+eDMcPGTKEzs8WvKNGjYK5n+tbHnT8N954Ix2v/+oSERGRwNDCR0RERAJDCx8REREJDF/3+Bw4cMBefPFFT/7444/D8eweGzOzhQsXwpzdtMbuF3Ldw/Dpp5/SbUhKSoq99tpr+R7/zjvv0G3sxupevXrBnM17xRVX5Pv95Ae6CYzdOMruwzIz+/jjj2HO7juqXr06zNn/ZRc0dr7NmjWLvmbr1q0wnzlzJszXrFkDc9dN4g899BDdVhDQvQh52E2Eixcvhnnr1q1hvnr1ajoHu1GaOXXqFPw//mbNmsHx7DMy4/fyPPbYYzBnn9OuXbvoHHXq1KHbmDNnzsCbktn8VapUofuqVq2ar/e1bNmyv3+Df7F06VJPlp6eTsfn5ubCey7YTfnsPh4zs4kTJ8Kc3bTPjo/d52JmlpWVRbchCQkJdvPNN3vyr776Co7/xz/+Qfc1cuRImLP7vaZNmwZzdiN/pJKTk+n9PMjAgQPpNlbow+6DZdfEJ554gs6B7tM6c+YMHa+/+IiIiEhgaOEjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGD4quqKiYmxyy+/3JOzJ3Kyp1K6TJ8+HebvvfcezFn1lJlZ3bp1fc/vx4ABA+g2drc+eyquq/KnIPlpL+C6K55VzLGnAbMqhQ8++IDOcccddzjeHYcekb5ixQo41vV4dFZdMG7cOJizJ46yJz2b+a/GyM7Oho+HZ4/kr1ChAt0Xq/jq3LkzzFnV2saNG+kctWrVotuQcDjsfPz+X+3evdvX/s3458eent6/f3+6r7lz5/qePzo62qpWrerJWcXOv//9b7qvV199Febsac/sKcmsIskMf0dYewazc+fowYMHPTmr6mJtW8zMvv32W5izakxWFfzmm2/SOXr27Em3ITk5OfD40O9GM/4UbTOztWvXwvz111+H+fDhw2HO2lJEKj09HT59m32GrspO1obq0ksvhTm7jrKn3DOun4n+4iMiIiKBoYWPiIiIBIYWPiIiIhIYWviIiIhIYGjhIyIiIoGhhY+IiIgEhq9ydrNzpXx/tW3bNjj2pZdeovspWrQozFl58/XXXw/z8ePH0znGjh1LtyEZGRmwZPeaa66B4xs0aED3xcq9u3TpAvN58+bl4x3+d06dOgWburKGfw8++CDdFyvxZZ/HiRMnYF6/fn06x2+//Ua3uaCGtkOHDoVj2WMSzMzuv/9+mLMyf1RGX9AKFy5MS9eR3r17022jRo2COfsM2TnKysAjUbx4cWvRokW+x//rX/+i2wYPHgzz5557DubsXHSV0TZu3Bjm3bt3p69JS0uDTX6Tk5PheFbabGY2ZcoUmLdr1w7m7Lr0xRdf0DmQqCj+qyM3Nxc2jWSuu+46ug01OzUza9WqFczZZ+66VrNrExMVFWWlS5f25OgxE2buUnr2OATWGJeVzLuaxvptwmp27tE1qNyc/axcjVhZI3G2Pli5cmU+3uF/R3/xERERkcDQwkdEREQCQwsfERERCQwtfERERCQwtPARERGRwPBV1ZWQkGC33XabJ3/33Xfh+BtuuMH3G+rUqRPMWeNCV0UJu8ueiY2NtZo1a+Z7PKoeysOqnlhTzPXr1+d73kiFQiFYjcEa+1111VV0X6yyiVX4ffPNNzB3NbdzNYFl0tLS7JNPPvHkbdu2heNdDQrZ58uqt+bPnw/zIkWK0Dluuukmuq0gXHbZZXRbkyZNYL5582aYo+/+/xVWJeRqlskMGzYM5gkJCTC/5JJLfM/hUqJECdiAd8GCBXB8uXLl6L4++ugjmD/22GMw99uQMxLFixeHVVesms7VaHrmzJkw91tBuWXLFrqNNctkjh07BquPO3bsCMc/9dRTdF+DBg3yNTdr2jp16lT6GlZJ7FK4cGHY4Jg1PXY18p0wYYKvnFVRu6Bmxa5qNv3FR0RERAJDCx8REREJDC18REREJDC08BEREZHA0MJHREREAsNXVVdGRoatWrXKk995551wPLuL34z3Z7n77rthXqhQIZgfOXKEzrFx40a6DbnoootgDzHWM2rDhg10X6zapH379jBnd+sXpNjYWKtTp06+x//44490G6uqYFV2fiukzMy+/vprX/syO1cxgyq4WK+u7777ju5rzpw5MGfVP6yvUFpaGp3DtQ3Jzc2F/XKKFy8Ox58+fZru66effoI56we0YsUKmDdq1IjO4deBAwdgr7BbbrkFjmdVP2a8Co1dF1z9hph9+/b5fs3p06dt69atnrx169ZwfGpqqu85ihUrBvNq1arBfP/+/XRfZcuW9T2/n/1MmzaNvqZNmzYwZxWJnTt3hvkDDzzwN+8u/xITE2kFF8K+my5+P/M+ffr4nsMlPT3dFi9e7MlZdTWr0DIzGzNmDMxZBTCr9GXVx2a4AtlVTau/+IiIiEhgaOEjIiIigaGFj4iIiASGFj4iIiISGFr4iIiISGD4quoqWrSoNWjQwJPn5OTA8a6KmV69esGc9VQZPnw4zF13k7OePAyrmKlSpYqv/ZiZffrppzBnlVKomsyM/2zNDPbdKkisksbMLDs7G+asSqtDhw4wd/Xqql27tuPdceg9XHvttXAs62lkZnb77bfDHPUCcylRooSv8S779++3kSNHevK4uDg43tWri1UlpqSkwPzZZ5+Fuau3DvveMomJibCys2LFinC8q3IUVaWYmT3//PO+chdXHy2mUKFCtOoK+eOPP+i26tWrw3zevHkwZ5VjDRs2zPf7iRSrPHrwwQfpa1iPv4yMDJiPGDEC5m+88Qado2vXrnQbcujQIXvttdc8eaVKleB49t00M5s9ezbMWe+rJ598EuZjx46lc6AKwr9TqFAhS0xM9OQlS5aE49HYPOznyyoMu3XrRt9TQdFffERERCQwtPARERGRwNDCR0RERAJDCx8REREJDC18REREJDC08BEREZHAKJB6aNbE8+2336avueSSS3zN0apVK5gvWLDA135cChUqBBvKLV26FI6fPHky3RcrZ3c1A0RYY0gzs++//97XvrKysmzXrl2ePDk5GY5v164d3RcrdWdlmJmZmTBnZeaRCofDsJHelVdeCcezZrJmZjt27IA5K8tln+0vv/xC52BN/5gKFSrY6NGjPfmHH34Ixx89epTuq0WLFjBv3LgxzFEZvZm7oaKrjBgJhULOZoR/xc43M7PmzZvDvGXLlr7ek4uryS5TuHBhK1++fL7Hu8q9WaNH1ryZNdgtSPv27YPnysCBA+F412eIGtaama1cuRLm7Fy8/vrr6RyHDh2i25BSpUpZ7969PfkzzzwDx7PHKpgZbXa6fft2mG/atCkf7/B/Y9f3SLBHXcyYMYO+hp3rrGkt+51w8uRJOgd65ENWVhYdr7/4iIiISGBo4SMiIiKBoYWPiIiIBIYWPiIiIhIYWviIiIhIYIT8VCWEQqFDZsY75p0/UsLhcKm/hjq+8wY8PrML/xh1fOeNC/0cvdCPz0zn6Pl+jPz4IinHFBERETkf6b+6REREJDC08BEREZHA0MJHREREAsNXy4qkpKSw6/H0f7V161a6rWTJkjBHLSPMjD7GPiMjg85RtGhRmK9bt+4wuunJ7/GlpaXRbXv27IF5UlISzNnju1mrBzOzs2fPwnzz5s2+jo/tx/XI7507d8L84osvhnlcXBzMixUrRudgP8MDBw7A4zPjx8haQxQqVIjOv3nzZpizz5Adu+s+OjZ/QZ2j69ato9sSExNhHh8f72v83r176Rzscfmu40Ovuegi/G801IIlD2tFwD4/do6WKgVPNSd2fP9v/jB69D87Rw8ePEjn2bdvn6/3xT5Ddq00MytTpown27lzpx0+fDiExkdHR4fRz7JKlSpw/642DOz6V6lSJZiz64mfNih5XOco+vzY+RYVxX/N/v777zCvXr06zNlxxMTE0DnYdXzDhg30HI2Pjw+j855d41y/C1nrH3YdK1KkCMxdvysQ1znqa+GTmppqq1ev9uTs4s16AZmZdenSBeatW7eGOVsYrFmzhs5xzTXXwDwUCsG71VNTU331v5o3bx7dNmDAAJjfd999MH/yySdhvmHDBjrHqVOnYN6gQQNfx8f2wxY3Zvw4OnfuDPO6devC3NVDh/1Mxo0bR6sN2DEeP34cjnf1LmrUqBHMe/XqBfNOnTrB/MyZM3SOEiVKwLygztFQCH7vzczspptugjnrcXXXXXfBfPDgwXQO1s+OHV9ycrItX77ck7NFyUMPPUTnnjJlCszvuOMOmNerVw/mrDebGV+sREVF0XM0JSUF9uBjvYgmTJhA52f909g/Zthn3qBBAzrHY4895smuvvpqOj4uLs6aNWvmyefOnQvHs+u0Gb/+jRkzBubsO1uuXDk6B8PO0ZSUFPvuu+88+euvvw73w77jZmbdunWD+dSpU2GOFqFmZpdffjmdA/WxMjNLTU2l52ipUqXs+eef9+Ts+s56BZrx3/XDhg1j7wvmrt8ViOsc1X91iYiISGBo4SMiIiKBoYWPiIiIBIYWPiIiIhIYvm5uTk9Pt2+++caT5+TkwPGLFi2i+7r22mthzm5Cu+2222DuusHYr/T0dPv66689eZMmTeD40aNH031t2bIF5qVLl/b1nmrXru1rfCTeffddmC9ZsoS+Jjo6GuaPPPIIzCN5QvjYsWNhPm7cON/7mj9/Pszfeust+pqVK1f6yln1wvDhw+kc7LvDZGRkwAKDDz74wNd+zAzux8zs119/hfkDDzwA8xo1atA5du/e7es9nThxAl430I2WZmbZ2dl0X3PmzIH59u3bYT506FCYu26MZdcGl1AoBL8/7OZ4dE3Kw25WZt/d2bNnw5zd2B2JKlWqwBuZjx49CsevXbuW7qtp06Yw79u3L8y3bdsGc1fVkevmYyQcDsPzjlUwfvzxx772b2b27LPPwpxVQ8+aNYvuy1XAwVx88cXwRmZW8NKjRw+6L3bz+sKFC2Fep04dmLPv7d/Nj+gvPiIiIhIYWviIiIhIYGjhIyIiIoGhhY+IiIgEhhY+IiIiEhi+qrri4+PhXfafffaZ74nffPNNmPfr1w/m7HHnBSk+Pt5XlcYvv/zie479+/fD/NNPP4V5xYoV6b7YI+79at++PczZY+HN+J36VatWhfnAgQNhPmLECDqHq90CEw6H7fTp056cPb7c9aj+ypUrw7xjx44wZ4+GR+8nz3/+8x+6DSlatCisiGRVkuPHj6f7qlmzJsz//PNPmLdr1w7mqKVBHtf5i+Tk5MDeVOy8mjlzJt0X+34OGTIE5qz6hVUWmfHegpFo2LAhzF1VR6z/FWqpYGZ2ww03wPypp56ic3z11Vee7MSJE3Q8wyorXZYuXepr/L333gtzVs1mxq+9zNmzZ2EPsdtvvx2Od7VzaNy4McxR9bRLbGws3ebqR8jk5ubCNj+sncTnn39O98WOsUOHDjBn/dlcLSjQe2XtZMz0Fx8REREJEC18REREJDC08BEREZHA0MJHREREAkMLHxEREQkMLXxEREQkMHyVszOsxM1l7969MGeld6zk+sCBA3SOH3/80dd7OnPmDGxyV61aNTj+nXfeofuaMmUKzKdPnw7zunXr+hpvZjZp0iS6DcnKyoIl1ykpKXC8q6Fq9erVYZ6RkQHzUaNGwXzkyJF0jkikp6fb8uXLPTlr5sjOQzOzl156CeasfJuVHcfExNA5WHM9VpZ78uRJWOr60UcfwfGXXXYZnfvMmTMw//nnn2GOmhaa8eaMZv7LnpOSkuz+++/35CgzczefZKXurGns1KlTYe56HEEk5ezsOtOsWTM4vnz58nRfixcvhjn7HrJz2qVFixaeLJLj7tq1K8xZ6b0Z/0zYa1iJtAtrgM1ERUXBayNrUvz222/TfbHjYw2Bu3TpAnNXM2C/j5QwO/e9RU1E2bWMlfKb8Wv/M888A/NKlSrB/L333qNzbN261ZO5yvj1Fx8REREJDC18REREJDC08BEREZHA0MJHREREAkMLHxEREQmMAqnqqlWrFsxZ5Y8Zb4p36623wvyDDz6AuavJo6txGxIdHU0ruJA77rjD9zbWOI1V92RlZdE5WAXDww8/DPMiRYrQCi5k1apV+R6bh1XZsQaXa9eupfsqW7as7/mLFy8OK7iOHTsGx7sqZvr37w9zViHGqhc6depE53j11VfpNqRYsWKw6d/GjRvheFeT0lOnTsH87rvvhvnTTz8Nc1eDS/a9ZY4cOQKrYNj34+WXX6b7Yt9lVFFlZvb777/DfPv27XQOvw0uzfh1hjUwdjVnfOihh2Det29fmF955ZUwd31O1113nSdzXZdOnDhhixYt8uSsIbGrESmrjmXq168Pc1c1m6vJLnLw4EF75ZVXPPkjjzziaz9mZn369IH5l19+CXNW3RxJ5ZZLYmJiRBVyCLtusEbXrBq7cOHCBfJ+zPQXHxEREQkQLXxEREQkMLTwERERkcDQwkdEREQCQwsfERERCYwCqepiXL2y4uLifO1r1qxZMO/Xrx99zYQJE3zNwXzyyScwb9u2re99bdq0Cea9e/eGeXR0NN2Xq89UQfjiiy/otjZt2sC8TJkyMGcVWvPmzaNzsJ5KLqyXFaqEilTt2rVhfvPNN8O8W7dudF+uqkQkMzMTVnCxXlaoh00eVtE2f/58mLNKIVThkgf1eXJJSEjw1TupXLlydBur0mL9hliPoH379tE57rvvPpizz8PMLDs7G1Y/sorPLVu20H2lp6fDvF69ejA/fPgwzFHlVh5UocXmNeOVleh7GSn2M9m1axfMI6lQZUqVKgWv16xvHOvh58LO0dmzZ8P8jTfeoPti52gk2DHu2bOHvoZVRT755JMwf//992Hu6geGromoL2Ue/cVHREREAkMLHxEREQkMLXxEREQkMLTwERERkcDQwkdEREQCo0CqulavXg3zI0eO0NewyphHH30U5h999BHM169f/zfv7r/HqrcWLlxIXzNmzBiYd+7cGeaPP/647/d1+vRp369B2HGwHmxmvFqIVQSxKoUVK1bQOcLhMN3GsF5WkcjJyYF5VBT+2lxxxRUw79q1K52DVR4xubm5sLKCVfi5Kv9Yj6KePXvCnPXKYd9ZM/+fYU3PUcoAAALgSURBVFZWlu3cudOTlyxZEo5v2rQp3RfrA7ds2TKYT5s2DeaDBw+mc0RSLVS4cGFY/ch+7m+++abvOVhvsx07dsC8cuXKvvY1adIkOv7EiRO2YMECTz5s2DD6Gubnn3+G+ZIlS2D+ww8/wJz1sotEKBSC1zNWodqxY0e6L/b98FvR6qqeZNcxl/3799vo0aM9Oeu79eCDD9J9sWvcgAEDYM5+Xg0bNqRzvPbaa56MnQtm+ouPiIiIBIgWPiIiIhIYWviIiIhIYGjhIyIiIoGhhY+IiIgEhhY+IiIiEhi+ytnPnDlj27Zt8+R169aF4zt06ED3dcstt8C8QoUKMGdlo65GZBUrVqTbkJMnT8Ly6t9++w2Ob968Od0XK7f85ZdfYF66dGmYX3bZZXSOxMREug05dOiQTZ482ZNfeumlcLyr1LpJkyYwb9CgAcwPHjwIc1cZfygUotuY7OxsWMLNSoL79+9P99WoUSOY16hRA+Zr1qyBebFixegcrDEmw47v+uuvh+NRSWqe1q1bw5yVk7KyWPZdjkRcXBxtsIncfffddBs7fy6++GKYf/nllzCvWrUqnSMhIcHx7rCsrCzbvXu3J2ePPRg5ciTd16BBg3zNzcrW0XU9T7Vq1XzNUbhwYXgdnzhxIhzPGjebmc2YMQPmJ06cgDm75rPmpWYF1+yZ/b6788476Wv8XuPuuecemLOfhxl/3IxLTEwM/b2AsO+OmdnRo0dhzhrNotJ0M7OUlBQ6B2r6m52dTcfrLz4iIiISGFr4iIiISGBo4SMiIiKBoYWPiIiIBIYWPiIiIhIYIT9NBEOh0CEz42VU54+UcDhc6q+hju+8AY/P7MI/Rh3feeNCP0cv9OMz0zl6vh8jP75IOmCLiIiInI/0X10iIiISGFr4iIiISGBo4SMiIiKBoYWPiIiIBIYWPiIiIhIYWviIiIhIYGjhIyIiIoGhhY+IiIgEhhY+IiIiEhj/A8IwAIyU2sBhAAAAAElFTkSuQmCC\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(10, 10, figsize=(10, 10), subplot_kw={'xticks':[], 'yticks':[]}, gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8,8), cmap='binary', interpolation='nearest', clim=(0 ,16))\n",
    "    plt.show()\n",
    "plot_digits(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "PCA(copy=True, iterated_power='auto', n_components=0.5, random_state=None,\n    svd_solver='auto', tol=0.0, whiten=False)"
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "source": [
    "pca = PCA(0.5)\n",
    "pca.fit(noisy_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "12"
     },
     "metadata": {},
     "execution_count": 29
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 720x720 with 100 Axes>",
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lypWDefXq1WHu6gfGfjTZ9pnxbWQ/EOzH34xfEIsXLw5ztu3ffPMNHYP1TvLdh+wHwtXnac6cOTDv2bMnzIsWLQrzkSNH0jEuu+wymBcsWJBu3/z586NyNgl2WbFiBcyvvPJKmLML/TvvvEPHqFmzJsxz587tPEbRNjJbt26lr+3evRvmHTt2hDnrPzdq1Cg6Bpr41atXj77f9zrjmhiwySv73tk/hL/44gs6BvvHZUJCgtc5yP6hv3TpUjo2+7ysz2X58uVh/sQTT9AxfH8nzH7bxgULFtB1/rcTJ07Q19i199prr4U567/5zDPP0DHQPqxfvz59v/6rS0REREJDEx8REREJDU18REREJDS87vGJRCLw/+t27doF3z979my6ro8//hjm7N4RdkOp6x4f101zyKlTp2znzp1ReYkS8P4vy5WLf32TJk2Ced26db0+05YtW+hrBQsW9FrX6dOn4U3l7D4Q9v/rZvz+LXazJ7tBE33fZ5QqVYq+xmRnZ9u+ffui8sKFC8P3u+4dGTFiBMzZvTzs/99Xr15Nx3DdlIhEIhH4/+nsfqT9+/fTdbH7x9hNhOzcZDcLm5k1btyYvoZkZ2fboUOHovICBQrA98+YMYOu6+uvv4Y52w52vwy7R8Hst3PKV05ODvwMaLvNeCGIGb8359dff4V5w4YNYZ6VlUXHQPeIuG5mPX36NFwfu8788ssvdF3st8U337RpEx3DddMswraPnWvsOzfj98ex+4Vuu+02mLvuk3IdvwzbxqSkJPh+dp+vmdnw4cNhzvYJKwZhN3yb4fvQXMeo/uIjIiIioaGJj4iIiISGJj4iIiISGpr4iIiISGho4iMiIiKh4VXVFQQBfMIwe/qtq9qDPUqfVUm47hpnfJ/2mjt3blhls379evh+VrllZvbuu+/CnFV1sYoOVlFmxiuVmFy5csG78qdOnQrfzx4pbsY/L6qoMuNVRxUrVqRjsJYRLomJifAJw5s344eUsqcXm5l98sknMG/SpAnM2aPWXdVpbBkXn+PaVdGxY8cOmJcsWRLmrEqCPY3czP+8TUxMtAsvvDAqnzlzJny/64nDixcvhjl7yiyrbHJV/bAnrrskJCTAJ/ay68zy5cvputj3wqqCihUrBnP2JGQzXL3qOjdz5coFn27OzqfJkyfTdbGnDvtiT6w240+IZ9j2sSrY9PR0uq5XX30V5qzykP1uspZOZrH9drJtZFXGP//8M13XkCFDYO7bjqRIkSJ0DNSWw3WM6i8+IiIiEhqa+IiIiEhoaOIjIiIioaGJj4iIiISGJj4iIiISGpr4iIiISGh4lbMzqHzYzGDJ5hms6SBrWnndddf5fzBPrAkrK4V+8MEHvcdgjRAbNWoEc1Z+asZLVl1QCSErd/zoo4/oelhDTvaZLr30Upi7Sg5jaQBphreRPVphwIABdD2srJs16mP7ylXO7moEiwRBAPcXW09GRgZdFysnZaW0rOSZfR+uMVzQMqzJ7cSJE+l6WFNMn3HN3M0O44k9poA1BDZzN6dEateuDfNYHqvgizV1/vbbb+kyTZs29RqD/ea4HgsS63Xmv23duhXmvXv3psuw6xJ7TMLChQthXqVKFToGKvU+F+i4Z41FWVm+Gd8WdrzH0iwYvaYmpSIiIiKmiY+IiIiEiCY+IiIiEhqa+IiIiEhoaOIjIiIioRGXqi5W/XLNNdfQZYYNG+Y1hm/1ixlvRsgEQQCrGypUqADf72rst23bNpjv2rUL5qwBm6uqKxboTnpWOdG3b1+6ntWrV8OcNRxk+49VEJnFXmmCtpFVj11yySV0PW3btoX5iBEjYJ6WlgZzV3O9fPny0dcYtH1sPeXKlaPreeihh2D+xhtvwJztK1ejTt9GwWyZxo0bw/e+/fbbdD2soo1VEbGqrszMTDqG6/v1xY5FVyNfVsX0zDPPwNxVGcOgqqdYKt369OkDc9c5+Nlnn8GcNcX86aefYO46z+JVtceOhZSUFLoMa8jJqmNR41BX/r9A5yHblgceeICuhzVQff3112HOGlq7GrGqSamIiIgIoYmPiIiIhIYmPiIiIhIamviIiIhIaGjiIyIiIqHhXdWFKh9Yr5N169bR9bBqhD179sD8gw8+gPnTTz9Nx4ilYgZhvazeeecdugyrenrsscdgPm3aNO/PFS9s/3Xr1o0uM3bsWJizHl5z586FuavqJ9YeMwirKrvxxhvpMqyaZubMmV75mDFjzvLp/nfbt2+H+YUXXkiXKVu2LMxZdVNWVhbM8+fPT8eIpRoTYcfozTffTJdhx9ysWbNgznrysapOs9j65TGs75ar56GrYhCZNGkSzF19B2OpekLLsO1r2LAhXY+rXyAyfvx4mNerV48u46r+8cHOG9c21K1bF+asJ1Y8qwhjcejQIZj37NmTLjNnzhyYswrg+vXrw5xdr8zUq0tERESE0sRHREREQkMTHxEREQkNTXxEREQkNDTxERERkdDwrupCVTjs7unDhw/T9bC701k/oHnz5sGc3cVvZta+fXv6mg/2WcuUKUOXadCgAcxnz54Nc1bN5voOWRWBr1KlSnkv06VLF5izyibWW4fd8W/mrvbw1axZM5iz6gkzs0svvdRrjNTUVK/3m5mdPHnSexmE9bFZu3YtXYZV2bBKLFdVBROviqACBQp4r4f1uWPVnpdddhnMCxYsSMdgFZ+xcFXHMVWrVoU523ZWRcn6mrF1ne3agyqlYtmH9957L8xZpSTrG+kSr8q85ORkmLPeU2b89+v555+Huas/JBOvyspYx2/UqBHMS5QoEbcxfH8L9RcfERERCQ1NfERERCQ0NPERERGR0NDER0REREJDEx8REREJDU18REREJDS8y9kRVq7Xpk0busyqVatgPn36dJhnZ2fD3FXujRqXxSJXrrh8TWZm9v7778OclfCxZqdmvJmbL1ejUIaVQo8cORLmrOHor7/+GtfPxbBmnZUqVaLLsKaVhQsXhnnfvn29P9cFF1zgvQzCzg9XU8OlS5fCfPfu3TBnDRVd+9D1yAcmXk0jWRnvsmXLYN68eXOYs+/DLLbtY9g+3L9/v/e6Tpw4AXNWur18+XK6LvRojng9SuNs2GMa2KMj2OM0WHm/mVmrVq28Pxfafvbdsma5ZmbVqlWDeY0aNWDOHgviOg5jKQ+PJ3b8Fi1aFObssRkrVqygY6BlXMeo/uIjIiIioaGJj4iIiISGJj4iIiISGpr4iIiISGho4iMiIiKhEfg0EQyCYI+Z4VKX80tqJBKJ6pCm7TtvwO0z+/Nvo7bvvPFnP0b/7NtnpmP0fN9Gvn2xdE8WEREROR/pv7pEREQkNDTxERERkdDQxEdERERCw6sXQ1JSUiQtLS0uA7N2AOyx7ewx1q5H/rP7lxYvXpyJbnpi28cefe16VH9mZibMK1asCPP8+fPTdflKT0+n24ce9c6+8127dtEx2LYnJSXBnLVOiKUtBdu+/3/8uB2jmzZtgjn7vthj8QsWLEjHYNu/dOlSr2M0Fhs3boQ5e/Q+247ixYvTMdj5uWzZst99+/bs2QNzduyyc9DVDiAxMRHmbP+Z8W1k1ytXC48DBw7AfP369TBnrWMqV65Mx0D7cOvWrZaVlQU/mO8+PHnyJH2NbR9rg8DOQdcxyq7vvr8TsWAtlzZs2ADzAgUKwLx8+fJ0jD/iGGXXSjOzffv2wZz9FrJWFr4yMjIsMzMTHqNeE5+0tDRbuHBhVM5+CNgXbmZ25513wnzv3r0wf+mll2Du2uGnT5+GecGCBeGsKy0tzebPnx+Vs54/b7zxBh171KhRMP/www9hfumll9J1+QqCAG5famqqzZ49OypnF5eBAwfSMdi233zzzTB/+eWXYc5OZDN+kiUkJNBqA3aMMuzYNTPr1q0bzI8cOQLzjh07wvzKK6+kY7Af26SkJHqM+myfS6dOnWC+du1amDdq1AjmPXv2pGOwCW+ZMmV+9+0bMWIEzIcOHQrz2rVrw/wf//gHHYNdpIsXL+59jLIJZ968een4EydOhPl1110H8+TkZJiPGTOGjoGusa1bt6bv9/2d2LZtG13Xd999B/Mvv/wS5uyYvv322+kYbPJRqFCh3/0YnTFjBsxvueUWmKO+aWZmgwcPpmMUKlQI5iVLlozbMdq9e3c6/vjx42H+z3/+E+bsOuqrXr169DX9V5eIiIiEhiY+IiIiEhqa+IiIiEhoaOIjIiIioeF1c3MkEoE3DOfKhVfz8ccf03WNHDnSZ2g7deoUzNkNUmZm1atX9xojEonAcebMmQPfP2/ePLquIkWKwJzd6BXPm5uZIAgsT548UfkPP/wA3//tt9/SdZ04cQLmn332GcyfeuopmLtubnZVs7j4PI387bffpq8tWbIE5jVr1oQ5OxZdVV3sJtR4mT59On2NVe21a9cO5v3794f5hRdeSMd47rnn+IcjUJUNq35z3Zy+Zs0amPfu3RvmbPuqVatGx3jsscfoay7oc7NijN27d9P1TJgwAeasumnr1q0wZ9cAM7OHHnooKnMVruTk5NjRo0ejclbJW6pUKboudu4sXrwY5ux3glUQmZldfvnl9DUkEonASjRXhTHDrrGs+o7t7woVKtAxXL+RDNvGqVOnwvcvW7aMrovdkI0KbczM6tevD/N4VdKZ6S8+IiIiEiKa+IiIiEhoaOIjIiIioaGJj4iIiISGJj4iIiISGl5VXQxrMzF37ly6zEUXXQRz9nj2adOmwTyWXk8Mq3pCmRl/HL8Zf4w/e8Q8q4BzPb6bVdP5YtUIHTp0oMuwR9+zVh0lSsCWMHHHKg9ZPyD2uHozXv3Dejd98cUXMGcVNma8eoPxrSipWrUqXRertEP93Mxiq3pi5068uKqL7rrrLpizYwFVL5mZXXbZZXQMV1WiC6pYZBVJrELUjFcksWsDOz8bN25Mx0D70FVxmZCQAFuxsOot1/nBvntWAffzzz/D3NWLLJZzEO2rWKq6Dh48CHPf4+qqq66ir7lanjCRSARWHtaoUQO+/7777qPrYn3HWDWoqwqW8ankNdNffERERCRENPERERGR0NDER0REREJDEx8REREJDU18REREJDQ08REREZHQ8KqHDoIAlkmyUjJXmStrRPbTTz/BvEmTJjBHDQ3jjZXddenShS7TsGFDmLMmnseOHYM5avZ3RuHChelrPlgz16uvvpouU6hQIZgfOHAA5r93WfMZQRDAEmdWssoeq2BmVrZsWZgvX74c5o888gjMXWWuriabjE/zVvbYATNeys8am952220wL126NB3j+PHjjk8XLRKJeDUpdWGl/G+99RbMn376aZizprRmZkeOHPH+XGZ4e9h3dejQIbqeHj16wJyVb7OydVdJOboGua677JES+fLlo8sw7Dfk5ptvhjkbY//+/XQMdi37I7DfiQULFsC8adOmMHeV67t+Qxh2HWWPumCNSM3Mhg4dCvOuXbvCPCkpCeaua4lvyb7+4iMiIiKhoYmPiIiIhIYmPiIiIhIamviIiIhIaGjiIyIiIqERny6XhKvqiDUuY3egDxgwAOauBnPxqviqXbu29zKsYeUHH3wA8xdeeAHmru+QVVD5clWtMF9//TXMWcVTLFil29mgihnWmHLdunV0PayygjUWvPvuu2Hu2oc+FVpn3o+OeVZdxM4bM7OpU6fCnK3rnXfegXmdOnXoGL4NIFnlaGZmJnz/sGHD6LrYObhs2TKYv/feezBPS0ujY7DjKhZZWVkwZ5/LzKx169YwT09Ph3m7du1gXrJkSToGajjqqrJj+3DTpk3w/ePHj6frYo1b2bpYY9qiRYvSMXwbgiYkJHgt8/7779PX2O/BwoULYf7GG2/APJZruEsQBF5NV9euXUtfY+upV6+e12eKpdkqo7/4iIiISGho4iMiIiKhoYmPiIiIhIYmPiIiIhIamviIiIhIaHhVdUUiEVjFsGfPHvj+kSNH0nWxihl29z2reHD1Wjpx4gR97ff2/PPPe70/JSUF5q5eTqyHmC9WSTdjxgy6TPv27WF+ySWXeI3t6qFTpEgRr3WZ/XaMov2+d+9e+P63336brqt48eIwr1KlCsxZhZarn5Or2gTJycmB+2vnzp3w/axPjhnv78M+U12Ej4kAACAASURBVLly5c7hE/4nVpXDsD5Pu3btgu+fNm1a3MZ29atifCpf/k+ov2FGRgZ87+eff07Xw/qqsYpW1lPJVbnKejH62rp1K8xd15nJkyfDvG3btjC/8cYb/T9YnLDfNNYDzsysRIkSMGd95mK5Jvr2y4vFK6+8Ql+rWLEizK+99lqvMcaOHUtfc/XNRPQXHxEREQkNTXxEREQkNDTxERERkdDQxEdERERCQxMfERERCQ2vqi7Wv6N8+fLw/exubjN+Jz+7y33RokUwZxVJZrH12PLBKmnMeA8f1p9k1KhRMP/444/pGK6KJB+s+o31cnIpVKgQzFnfpJUrV9J1PfLII97jB0FgefLkicpZxU5SUhJdF6tWvPrqq2E+c+ZMmLv6VbHqOCYhIQH2TipdujR8f926dem6WOVPy5YtYb5t2zaY79ixg45RoUIF+hrC+jyxKpcOHTrQdbFKPubw4cMwHzNmDF2mefPmXmO4sGtDq1at6DKskpDlrh5bTLyqulgFbtOmTeky1atXh3mbNm1gvmbNGpiz3pBmZs2aNaOv+WCf9YYbbqDLsN9IVu3KfnNYRZmZWdmyZelrDKuuZD3Sli5dStfFKrLZ70v//v1h7qpoQz3r0Oc/Q3/xERERkdDQxEdERERCQxMfERERCQ1NfERERCQ0NPERERGR0NDER0RERELDq5ydKVCgAMzff/99ukylSpVg/s4778CclUM3btyYjsFKfJmcnBw7duxYVM5K09lnNeMNEnfv3g3zPn36wNxVbp2enk5fQ3JycmDDTFauevDgQbouts9ZyeFXX30Fc1SafcbatWvpa74KFiwI8x9++IEu89hjj8F83LhxMGel/K6SdXS8xYJ9jz/99BNd5tFHH4U5K03NzMyE+eWXX07HcD3SwkdiYiLMH3jgAbrMp59+CvPBgwfDfPTo0TDv3LkzHSPWcnZ0zrFHLriaPa9YsQLmr7/+OszZ8eA611E5PXsUggs7P1hpuhlvFPzGG2/AfN68eTB3PdokXo89Yds3bNgwugx7hEKtWrVgHkvD0e7du3svEwQBPOfY42bYIz7M+DW2RYsWMGfNtx966CE6BnqECXukg5n+4iMiIiIhoomPiIiIhIYmPiIiIhIamviIiIhIaGjiIyIiIqER+DSgC4Jgj5lt/v0+zh8mNRKJRN2eru07b8DtM/vzb6O277zxZz9G/+zbZ6Zj9HzfRr598eq8KyIiIvL/Ov1Xl4iIiISGJj4iIiISGpr4iIiISGh4taxISkqKpKWlnfP7t2zZQl9jj0hnj94vVaoUzFnrBJf09PRMdNMT2z52HxRrP2HGHy2+d+9emLPHdLu+b/YYf9/tY4+f37FjBx173759MM/OzoZ53rx5YV6+fHk6BjsWFi1aBLfPzH8fbtq0iY7PjtFcufBpw1qksMfuu8RrH7q27+jRozBn+4q1VGC5GX9sfLzOwa1bt9KxT5w4AXPWTqZo0aIw9219Y8a3z8x/G3/99Vc6zq5du2B++vRpmLPrTNmyZekY6HjYvHmzZWZmwp3Lto9dG9atW0fHZsc1y9k+dG0f43uMsu1buXIlHYNtB7tmsN/BCy64gI7BxHKMMuz3wIz/jrDfyHLlysGcbTuTkZFBj1GviU9aWprNnz8/Kk9IwH84uueee+i6WM8Y1jfl4YcfhnmjRo3oGEwQBPBu9bS0NFu4cGFUzi6gr732Gh1jzZo1MP/www9hzvqWuPqBsb5YvtvH+kU9++yzdOzx48fDnJ0A1atXh/mQIUPoGHXq1IF5njx5aLUBO0bZD0HXrl3p+N9//z3M2Qn45JNPwrxHjx50DCZe+9C1fYsWLYJ5jRo1YH7LLbfA/LbbbqNjsEmi7/axyQq7LpiZbdy4EeY7d+6EeceOHWH+1FNP0TEYtn1mv23jggULonJ2jA4dOpSO89JLL8Gc9VVr2rSp13rM8LnbsGFD+n62D9k/JNq2bUvXxSbn7Hhn+7B///50DMb3GD1w4ABcD+u7ZcZ7dd16660wf+SRR2CekpJCx2DOdoyibWT+/e9/09f69esHc/Yb+eCDD8Kc9U5k6tWrR1/Tf3WJiIhIaGjiIyIiIqGhiY+IiIiEhiY+IiIiEhpeNzdHIhE7efJkVL5kyRL4/tWrV9N1sZvjfvnlF5izm/XiKRKJwJsoWWUMq6gw43fZo+/PzGzVqlUwd1V0sJubfW3fvh3m33zzDV3mkksugTmrBHjrrbdgvnjxYjpGgwYN6GsuqJJo+fLl8L1s283MWrVqBfMffvgB5kuXLoU5uznezCxPnjz0NYQdo+wc3LBhA13XtddeC/N58+bB/KOPPoJ548aN6RhVqlShryHsGvPzzz/D97uqWdq1awfzMWPGwJzdaOo6z5OTk+lrLugYZdUv7Nwx86+AmT59Osz3799Px0A3qLNqPbPf9iGq2GHXONfY7BwcMWIEzD/77DOY33XXXXQM9h0yOTk58OZqdg6y6lszs6+++grmrOiDFZz87W9/o2NUq1aNvuZr/fr1MH/xxRfpMmXKlIE5q2IcMGAAzG+44QY6hu91Rn/xERERkdDQxEdERERCQxMfERERCQ1NfERERCQ0NPERERGR0PCq6jLD7SlYZcOjjz5K18NaVrAKiiZNmpzDp/tPrmoaJAgCWMHAekb16dOHrmvUqFFeY1999dUwr1ixotd6YsF6LQ0cOJAuw1qFsOqb9PR0mLPqsP8Fqha46KKL4HsnTpxI1/Pxxx/DnFWOsCop38otF3aMlixZEr6fVUiY8Som1qqD9XmKpRcZEwQBrNRi+49V/ZjxKiJWGXP33XfDPNbKLV+s+qdv3750mWbNmsGcPfaf7auqVaue5dOduyAI4DHPxna1y2C/E6wVCqsWZsduLBISEixfvnxROatoZVWgZmaVKlWC+b/+9S+Ys2sPO3bj7ciRIzB3teW5//77Yd69e3eYs3ZIJUrAtmIx0V98REREJDQ08REREZHQ0MRHREREQkMTHxEREQkNTXxEREQkNDTxERERkdDwLmfPycmJylgZH2tCZmZ20003wTwpKQnmCxcuhHnz5s3pGLGUEaPtK1u2LHwvKwc2M5szZ47XuDVr1oQ5K9uMJ1bOfv3119NlWIkma2R54403wrxWrVpn+XR+IpGInT59OipnjyRguRlvIMi4jod4iUQilp2dHZWzsliWm/EmnqwRYdeuXWFesGBBOoYv1oTVt5Gkmdnnn38Oc7afChcu7D0G2hexYo1Fe/XqRZf597//DfNJkybBvHPnzjBn14BYsHPQt5GkGb9uMH/5y19gXqhQIe+xmUgkAh+Vwq4lrjLsAwcOwJz93jHbtm2jr8XzGlu6dGmYs5J1lxUrVsC8S5cuMI9XU24z/cVHREREQkQTHxEREQkNTXxEREQkNDTxERERkdDQxEdERERCw6tkKAgCy5079zm/n1VDmZlt2LAB5jt27IA5q94aNmwYHcNVDcGgRoGoQsHM3fjuzTffhPngwYNhzqqhWDNQM7PatWvT135vV155JczZ3f3sO7z33nvpGGyZs0GNdGPx3nvvwfzVV1+FeYcOHWDOKm9cyzCsSWksbrvtNpizc5A1mURNRWPle41xSU1NhTmrQn3qqadgzhqkmplVrlzZ+3MxsexX1sSYVbSOGzcO5q5rJWoQ7arY9d2Hrmovdg6yc2r//v3nPO7/IgiCqIxVaMXSXJNVGLK8fv36dF2ooWqsfBt/m5mtW7cO5osXL/Z6v6sRa40aNaIyVKF9hv7iIyIiIqGhiY+IiIiEhiY+IiIiEhqa+IiIiEhoaOIjIiIioeFdRoCqnpgtW7bQ11g1REpKCsxZPyBWPWVm1q1bN8enO3c7d+6EuauyoWrVqjC/5pprYM6qKlz9n1BPI5ecnBw7evRoVO7qV8Wwqg1W7cX6JrE7+83clQoMq3pi1R4nT56k62J9aV5++WWYv/LKKzCfPHkyHYP1y3JB1QqxVLKxfTVr1iyYz5s3D+YdO3akY7Dee7727t0L87x589JlLr74YpgPHz4c5qxab+nSpXSMatWq0deYSCRix48fhzniqsqpXr06zNkx+sILL8A8IyODjsGOExd0jB46dAi+F30XZ/To0QPm8+fPhzm7jnbv3p2O4Vs9GgQBrGQ8duyY13rMeGUwqhozMytfvrxXHit2jLLr5ffff0/Xxfqk9ezZE+askm/lypV0jHr16kVlrmui/uIjIiIioaGJj4iIiISGJj4iIiISGpr4iIiISGho4iMiIiKh4VXVFYlEYCXRwYMH4fv/8Y9/0HXdfPPNMC9XrhzMMzMzYd60aVM6hqtXh48CBQrAfPTo0XQZVu3xxhtvwJxVBLju1md3/jMJCQmwgot9Tx988AFdV7FixWA+YcIEmO/Zswfmrt468ey7w7Zx4MCBdJmaNWvCfM2aNV5joz4yZ7gqAxlUrcDOQVbdY8YrD6dNmwbzTZs2wZxV3piZ1alTh77mgx3rEydOpMuwipmNGzfCnFWNbNu2jY7BvneXIAic1Wj/bcGCBfS1Dz/8EOZsW1ilYoUKFegYqJL3bNcen2PU1SdswIABMGeVebFAla6xKFOmDMwnTZpEl2FVvuwaw75313UkKyuLvsawY5T9Hv344490XexYXLt2rddnYj0EzXDFoHp1iYiIiJgmPiIiIhIimviIiIhIaGjiIyIiIqGhiY+IiIiEhiY+IiIiEhpe5exBEMDmlKgp5NncfffdMN++fTvMWXm4q6zRp2TUhTXxdJVBskZrmzdvhvmgQYNg7ipnj6UUGi1z4sQJ+N7ly5fT9QwePBjmrMz9mWeegTlqLneGq3mhL3aMrlixgi7DmlYWKVIE5k8++STMH3roITpGLPsQYU1jlyxZQpcZMmSI12diZevFixenY8SrVJh9ps8++4wuw8qn9+3bB/OGDRvCvGXLlnSMWJrDMqwB5E8//USXef3112F+4403wvzRRx+FuWsb0aM2YnlUSKlSpWB+4MABukzbtm29xnj33Xe93m8Wv32IGpeambVv354uw5pvd+7cGebsOsqa+Jq5y8B9sW0sXLgwXeajjz6COTuGWOPmNm3a0DHQdSY7O5u+X3/xERERkdDQxEdERERCQxMfERERCQ1NfERERCQ0NPERERGR0Ah8qkqCINhjZrgs6fySGolESvx3qO07b8DtM/vzb6O277zxZz9G/+zbZ6Zj9HzfRr598SqnFREREfl/nf6rS0REREJDEx8REREJDU18REREJDS8ek0kJSVF0tLS4jLwqVOnYM4ecX/hhRfGZVwzs/T09Ex001Px4sUjKSkpUe9PTEz0HuPw4cMw379/P8zLlSvnPQbDti+e+49ZvXo1zNnj6lmLCxe2fWa/bWNqampUHgSB9zjsUe9sXaVLl/Yeg3HtQ3SMss/k2u7MzEyYs1YPFStWpOvyFa9jlLV5MDPbs2cPzFmLgj9i/5n9dp3xOUZd92Fu2rQJ5mxd7DrjatuA2r1kZGRYZmYmHCSe+5Adi6zNTnJyMsxjuYb/EddR1j6F5X/EOWjGfwvZceVqD7Fx40aYs33IjlHWOsrMLE+ePFHZ5s2b6THqNfFJS0uzBQsWROXx/FFhvYWuvfZa7zGYIAjg3eopKSn2888/R+WFChVi66FjzJ49G+ZffvklzP/1r3/Rdfli2xfP/cc0aNAA5g888ADMb7vtNu8x2PaZmaWmptqsWbOi8lj6trG+OKxfTb9+/bzHYFzH6IwZM875M7EeXma8r9GkSZNgPn78eLouX65jdP78+ej9cD2s952Z2ciRI2HOLqCs11osP5pnO0bRdQZdvM3cE4Pu3bvDnO33V155BeYFChSgY6DedOw8N/O/zmRkZNB1TZ06Febr1q2D+eOPPw7zokWL0jEY32M0lp5frNccO9fGjRsH81iu4a5jNCUlBX737Fxw9eS7+eabYc7O3f79+8O8Tp06dIyqVatGZaz3npn+q0tERERCRBMfERERCQ1NfERERCQ0NPERERGR0PC6ufnUqVO2c+fOqLxMmTLeAw8cOBDmhw4dgjm7udlV8eD7VOpIJALvNC9cuDB8/7Rp0+i62I2VrAojFq476ZHTp0/b3r17o/LixYt7j33PPffA/Pjx4zBPSkqC+a5du+gYsVTyRSIRr/2OblI8g91k9/LLL3t9piNHjtDXfG+6DoIA3mDIbmZl55OZWa9evWDeqFEjmLMqDNdNna6bq5GcnBx4oyS78Zfd/Gpm9ssvv8C8RYsWMGeVNKiq6QzXTcFMQkICXI7dIHrvvffSdX3xxRcwb9KkCcwPHDgA8/Lly9MxcnJy6GtIdnY2HAfdJG3mrmhlxS5sGXYTc1ZWFh2DfS6GHaMFCxb0Wo+Z2UsvvQRzdgP+9OnTYX7ZZZfRMdi545KYmAi/F1atfOutt9J1zZw5E+aDBw/2WpfrJn9f+ouPiIiIhIYmPiIiIhIamviIiIhIaGjiIyIiIqGhiY+IiIiEhldVF7vTm0GP1j9jyJAhMH/rrbdgzu4mnzdvHh2jadOmjk8XLVeuXFaiRHTrElb507x5c7ou9njtTp06wfyJJ56AedeuXekYtWrVoq8huXLl8uqNxdpumJkNHz4c5j179oQ5qiYzc1cdsb47LgkJCZYvX75zfn+rVq3oa6zShbXZeP7552Huqrho3bq149NFC4LAqxKsQ4cOXus3M3v77bdhzips2L41M7vmmmu8xk5ISIDVMezx9qx60jV2jRo1YM6q+Lp160bHqF27Nn3NBVXCsevl6NGj6XpQPyUzflyzqtIKFSrQMXwr13x/J3744Qf6GrsGsesiq/JjlblmZtWrV3d8umisKo9h55OZ2YoVK2DOfg8mTpwIc9c1r379+o5P52fOnDkwd1VXvvfeezDv0aOH19iszZXZb21g/purjYf+4iMiIiKhoYmPiIiIhIYmPiIiIhIamviIiIhIaGjiIyIiIqGhiY+IiIiEhlc5uxlu/Llhwwb43mbNmtH1XHzxxTC/4YYbYN6nTx+YV65cmY7RsGFD+pqPzz//3HuZZ599FuasKeeTTz4J84suuoiOwcpymUgkYqdOnYrKV65cCd9/880303V17twZ5qw0dNmyZTBnZf9mZseOHaOv+WJloAcPHqTLDBgwAOasPPO5556Duauc1dUAk0HnIGuY6yoVHj9+PMzZcXXHHXfAnDXENPutMW48LF68GOZz586ly9x9990wHzt2LMynTJkCc1dJvqtk1perYS/Tvn17mLNrMmv8yxrTmvmXs0ciEdhQcs+ePfD97DEQZrzB7yeffALzd999F+auxsK+5yDbPtbk9o033qDruv3222HOGnJ+9913MHc9ugVd82M1efJk72VY2TprIsxK412/567HMSD6i4+IiIiEhiY+IiIiEhqa+IiIiEhoaOIjIiIioaGJj4iIiISG1+3sQRBYnjx5onJW5eLCGj0eOHAA5mvWrIF527Zt6Rio2aELq3pi1QguaWlpMP/www+91sPu7jczy507t9e6giCwCy64ICpnlQI7d+6k62KNKVnzUrZfXRUzvlVrLkuXLvVe5pVXXoE5a5hZtGhRmLsq83yxY/S1117zXhdrWNmlSxeYf/zxxzC//PLL6RixVK0hrDFru3bt6DKjRo2C+cyZM2F+/fXXwzyex6HLpZdeCnPW+NeMN1DesmULzDt27AhzVwXl8ePHozJUWXgGu86wBpeuarasrCyYr169mi6DlClThr6GftNc2Pax30HW3NfMLDs7G+a7d++GOfstcu0/9FnPBfpsrv3OsMbcrFqaVUq6qmPROer6rPqLj4iIiISGJj4iIiISGpr4iIiISGho4iMiIiKhoYmPiIiIhIZ3VReq0sifP7/3wImJiTCfMGECzMuVKwfzePYJCoIAVkqxvmKDBg2i61q7di3MP/vsM6/P1KtXL6/3xyJfvnwwT0pKossULlzYa12syqRKlSpn+XR+WNUTq6xiPeDMeH8xVtXFetNdccUVdAxW1cGwczAlJcVrPWa8MuaLL77wWk+bNm3oa/HqE8TO/8cff5wu41vpxvZf+fLlvdZzNpFIBFZKlS5dGr7f1c/Ot6KWVbqyHl5m/Frti11PXn31VboMq8ZkFZfsu2JVtrFClUesqtMlOTkZ5mw/sbxSpUp0jFj65eXk5NiJEyei8hYtWsD3u6o3J02a5DU2q2KsW7cuXQZVfbr66OkvPiIiIhIamviIiIhIaGjiIyIiIqGhiY+IiIiEhiY+IiIiEhpxaaTD7sJ23en94IMPwvyWW26BObtj3lVxEa+Kkvvvvx/mrl5ZmZmZXmOw6rR49Tpy6dGjB8zr169PlylRogTMWRVa9erVYV68eHE6hqtPGcMq82688Ub4fpab8YqhuXPnwrxbt24wd1VuocqJs0lIiP73yoABA+B7XdUs+/btgzmqODLjffFSU1PpGPFSs2ZN72VY1dq6detgXrVqVZiz6j6z2KqFgiCAVSisH1nTpk29xyhbtizMS5UqBXNWqWhmVqtWrajMVTHDXHXVVd7LsD5wn376KcxbtWoFc1dlEzsPfHXv3h3mrNLVzOzIkSMwZ33mWrZsCXPXOZiTk0NfYxISEmC1NuuN5+qZN3LkSJizKr833ngD5vH8LdRffERERCQ0NPERERGR0NDER0REREJDEx8REREJDU18REREJDQ08REREZHQiEt9GCtJfuKJJ7zX9fXXX8O8b9++MN+0aRNdFytP9eUqW2dYKS1rSvfAAw/A/NChQ3SMWEpKEdag0NVck2FNBTt16gTzrKwsuq4yZcp4j/9HaNSoEcxZSenOnTvpuvLkyROXz8Saxj766KN0meHDh8O8SJEiMH///fe9P1e8sEcCbNy4kS6TkZEBc7afXNcSJpbGlL5cTUqvueYamLPS34ULF8KcXZfM8CNDfJvrmvHHU7CGzmZmCxYsgDkrhb7kkktg7mq0Gq8yadas+/bbb6fLzJgxA+a7du2COXssiOs36oILLqCvMazZcyQSge/ftm0bXRcr52cl+3/EI1z0Fx8REREJDU18REREJDQ08REREZHQ0MRHREREQkMTHxEREQmNgN2lDd8cBHvMjHezO3+kRiKRqC6b2r7zBtw+sz//Nmr7zht/9mP0z759ZjpGz/dt5NvnM/EREREROZ/pv7pEREQkNDTxERERkdDQxEdERERCw+vZ0ElJSZGUlJSoPCEBz59+/fVXuq6DBw/CnD1anLUviOWR/+np6Znopie2fTk5OXA9rlYErNXE8ePHYc4eOZ6WlkbHKFSoEMxd24fWhx5NbuZ+hP+xY8dgztqXsLYY7DHvZvxYYNtn5r8Pt27dSsc/fPgwzNmj91kLkYoVK9IxWHuIeB2je/bsoWMfOHAA5qwdAdtXJUrAXWFmZgUKFID5okWLvI7R06dPw/WwthSuZdj1ij3av1SpUnQM9jj+eB6ju3fvpuOzli/ssf/smlGsWDE6BtqHGRkZlpmZCQ/4pKSkCGoLwq4zrnOQ3YPKzkG2b8uWLUvHiOU6ytqeIK7fiaNHj8Kc/U6ULFnSK3c52zGKzsNYrqPst57JmzcvzF37EF2bXMeo18QnJSXFZs6ceU6DmpkNGzaMrmvKlCkwZz8Ezz//PMwrVKhAx2CCIIB3q6ekpNisWbOicvYj379/fzrGDz/8APNffvkF5mxiN2LECDrGVVddBXO2fWlpabBXD+sL06VLFzr28uXLYd6tWzeYt2vXDuauPkRsssS2z+y3fYj637B9+PDDD9PxWR+dzZvx8GwSPmjQIDrGDTfcAHPXMeqzfW+++SYde/LkyTBnk3a2r/r06UPHYH3NcufO7XWMZmZmwvX06NGDjs2WYT90qCeVmdkjjzxCx6hZsybMz3aMousM+xF85ZVX6Phjx46FOfsHSIsWLWDesWNHOkaDBg2isoYNG9L3p6am2pw5c6JyNoFjfQrN+MSHTXjZRPSll16iY/heR1NTU23u3LlROfsHw4svvkjHXrZsGcxZr8f77rsP5vfffz8dg3Edo2lpaTZ//vyo/MSJE/D9ruso+61n/1CsUqUKzP/5z3/SMdC1qV69evT9+q8uERERCQ1NfERERCQ0NPERERGR0NDER0RERELD6+ZmM3xXN7vhid08aWa2fv16mLMbD9ld47Hc3MwkJCTAm+PGjBkD3z948GC6rtKlS8Oc3eRbrVo1mNeqVYuOwW6mYyKRCKysWLVqFXw/ukHxDHbTasuWLWHetGlTmLMbaWOVkJAAq1CmT58O389uDjUzq1u3LszvuusumLObm9kNsGb85k2Gbd9PP/0E3z906FC6LlahwW4ubN++PcwvvvhiOgarLmIikQis2FmyZAl8/9KlS+m62DGXnJwMc1ZgwCouY8WuM+xGV9dNnQyrpmMFA9WrV6frYtWVLujG1R9//BG+98svv6TrYTfzsn1Yo0YNmBctWpSOEQt03m7fvh2+11XxtHfvXpg3adIE5uy6+3tAFXJsH7qKcJo3bw7zv//97zBfu3YtzF3Vo+h3zXVt1V98REREJDQ08REREZHQ0MRHREREQkMTHxEREQkNTXxEREQkNLxKLoIggH002KPI2V3uZmZr1qyB+dVXXw1z1r/DVRUUr2qMefPmeS/DHpHO+l+x6gX26PlYBEEAvxNWecMqJ8x4q4W2bdt6faYdO3bQ1woWLOi1LpcNGzZ4L/Pee+/BnH1frKKE9fwy4xWRvlglhOv8YO0ejhw5AvMbb7wR5vGsegqCAPbMYr2ZXP172GuseuuSSy6BOas0NfOvrHRZt26d9zKXX345zH0r89j1NRbsOsOq1ljrAjPeDmXbtm0wZ9sRz6oudoyySjrWhsmMf15WZedqw8DE8xh1VagxAwYMgDlrgcOOXdf36LuN+ouPiIiIhIYmPiIiIhIamviIiIhI/p5wBQAAIABJREFUaGjiIyIiIqGhiY+IiIiEhiY+IiIiEhreTUpR4y/UzMyMl/e5LFiwAObvv/8+zJ955hm6Llc5tg9WXucyfPhwmLPy5eeee857jHg5ePAgzFkDPTOzuXPnwrxLly4wZw3mWJmyGW+iGQtWou3Sr18/mLPPzB5JwB7RYBa/MmJW6ukq92Yl8Kx8e8+ePTBnDXnN3KXKPtj35DpGX3nlFZizMlrWDBSVLp/Brn2xYI+ucH2/7Dxkj4Jg58GBAwfoGKihaixOnz4Nc1czSdaElq2LbbfrsSDs8Qa+jh49CnNWem9m9v3338OcPQLj8ccf9/5csTSZZWJ5xEiHDh1gnpKSAvM333zT6/2M69qjv/iIiIhIaGjiIyIiIqGhiY+IiIiEhiY+IiIiEhqa+IiIiEhoeDcpRc3nWPXW2LFj6bpYJdGECRNgzqq3rr32WjpGu3bt6Gs+/va3v3mv/8knn4T55s2bYb5v3z6Yu5rrxdLgElVQFCtWDL63ZcuWdD2s0oPtc9bgkjWG/F+gbWzRogV872uvvUbXwxrpfvHFFzBnDRXZMW1mdumll9LXfPTs2RPmtWrVosvMmDED5uxYZM2IXVVPrsaCPtj+GzhwIF3mhRdegDk7dlljyKSkpLN8uvhgDX7fffdduszixYthftFFF8Gc7Y9Yqh599e7dG+bNmzeny9SsWRPmP/74I8wrVKgA88qVK9MxWNNhX6wSy1UVXL58eZjPmTMH5tdccw3MJ02adJZPFx9du3aFef78+eky9957L8znz58P8++++w7ml112GR3j1KlTUZmrWlB/8REREZHQ0MRHREREQkMTHxEREQkNTXxEREQkNDTxERERkdCIy+3srBdIWlqa97rY3eFPP/00zGfPnk3XddVVV3mNnZOTA/utsM/EKg7MeG+YHTt2wJz1pHFtQ548eehrSCQSgT1uSpYsCd/funVrui62DOupdvz4cZiz6rdY5eTkwLFYdVP9+vXpulgvK1bdtHXrVpiXK1eOjuHbR4ftQ1aZ0qBBA7qud955B+as/xWrhmJVgWbuygr2flShgapJzcxuuukmui5WqcT6HbG+SX/961/pGLGIRCLwGGX9yC6++GK6LlZ5uG7dOpizCrwrrriCjoE+q2u/smOUXRNdlYeswuehhx6COauAu/LKK+kYsUDbz3rcNWvWjK6nTZs2MO/fvz/MJ0+eDPNly5bRMWrXrk1fY3JycuD5wyq4//KXv9B1sX6BjzzyCMxZ/7nt27d7jaFeXSIiIiKmiY+IiIiEiCY+IiIiEhqa+IiIiEhoaOIjIiIioRGXqi5WKcCqRsx4tQnrRcK4+nf4VswEQeDVt4VVVJiZTZ06FeasgoFVdOzcuZOOUbp0aceni+bba41VuZiZNWnSBOasCsP3s5rxSjCXhIQE+F267vBnPv30U5ivXLkS5i+++CLMk5OTvcf2lZ2dDfMNGzbQZdj+rVatGszZMYqqsM7wrTxkxyjrg8SONzN+/Ozfvx/mru1gUPVSrFBFqZnZuHHj6DJvvfUWzFml3d///neY+/ZUc51P7DpauHBh+P6srCy6rl27dsGcHe81atSg64ontP2+lbxmvDr2hx9+8Po8rp6Ohw4d8lqX2W/XUfa7gLAqQjOzefPmwZzNG1hvPHYssGXUq0tERETENPERERGRENHER0REREJDEx8REREJDU18REREJDQ08REREZHQiEs5O2sgmJDA51XXXXcdzFkjsttvvx3mruZoviKRCCyTPHjwIHz/iBEj6Lq2bNkCc9bwkDVCdX2HrKSTYU1YWcmxqxT6888/h3nz5s1hPnjw4HP4hP8plhJ01uSSNazs0aMHXdeECRNgPmXKFJi3atXq7B/wf8S278SJE/D9H330kXNdCGucyJowxlIu6/pMqEQ8JycHvp+Vc5uZLVmyBOZdunSB+Z133nkOn/A/xVICz0r22T7ct28fXVdGRgbM27VrB/Mbb7zx7B/wf5SdnQ2vmey76tixI10Xe5wHK/GvU6fOOXzC/3TgwAHvZRBWnu167Mlzzz3nNcb48eNhXr58ea/1nA07D9kx+tJLL9F1vffeezBv27YtzNn56Xp0DaImpSIiIiKmiY+IiIiEiCY+IiIiEhqa+IiIiEhoaOIjIiIioRG4GnlFvTkI9pjZ5t/v4/xhUiORSIn/DrV95w24fWZ//m3U9p03/uzH6J99+8x0jJ7v28i3z2fiIyIiInI+0391iYiISGho4iMiIiKhoYmPiIiIhIZXy4qkpKRIamrqOb+fPWbezOzXX3+F+eHDh2GenJwMc/YYfZf09PRMdNMT275YWifs2bMH5nv37oV5mTJlYJ4vXz46RmJiIswXLVoUl+1z3f+1fv16mLM2GhUrVoQ5e8y7C9t/Zr9tY1pamvc6EXaMsm0sXbp0XMY1cx+jKSkpUe93tTZhdu/eDXPWIgGNa8bbrbi4ti9e+48do+y4LleuHMxd5yBbFzsHzeK7jZs2bYI5uzaULVvW6/1MRkaGZWZmwguH7/a52n5s3LgR5iVLloR50aJFz3ncM3z3YTyvo6zlCDufWWuKWM7/P+o6umPHDpijlhhm/Bh1bSP67l3HqNfEJzU11ebMmROVswnOyZMn6bpef/11mM+cORPmffv2hXmLFi3oGEwQBPBu9dTUVJs7d25UznqRuYwcORLmH3/8Mcz79esH80suuYSOUaRIEZjnzp2bbh/af7ly4cPAtf9Yzx/W14z1jIrl5GL778z6FixYgJbxHmfYsGEwZ9v41FNPeY/BLooJCQlwG1NSUmzWrFlRuevHmRk0aBDMv/jiC5gPGTIE5nXr1vUem+3DtLQ0W7hwoff6kBtuuAHm7Lh++eWXYV6zZk06BvvRvuCCC5zHaLy2kfU1Kl68OMz79+8P8wsvvNBr3Hr16tHXfLdv165d9LXOnTvD/O6774Z5p06dznncM44fPw7zfPny0evo7Nmzo3J2HWU/8GZmvXv3ZmPD/LXXXvN6v8vZrqPz58+PymOZYD377LMwZ38cePHFF2Hu+gcWmrg3bNiQvl//1SUiIiKhoYmPiIiIhIYmPiIiIhIamviIiIhIaHjd3Mywmz2nTZtGl3nmmWdgzm5Oa9asmffnclULIEEQ0BvUfN15550wf+GFF2DesmVLmLtu/PMVBAG8UTsrKwu+v0ePHnRd3333HczbtGkD89WrV8PcdXOz6+ZqJicnx44cORKVFyxY0HsMdnPzrbfe6v25GNeNjwwqJti8Gd+nOGLECLqegQMHwrxBgwYwj6Viht046iszMxPmw4cPp8tMmDAB5ujGVDP3TczMsWPHvJeJRCJwv7NrDyuUMOPFEp9++inMWRWlaz+hwgBXpRLbvnXr1sH3P//883Rd7Li++eab6TLIiRMn6GuxdC9A3wn7Du+55x66njFjxsD88ccfP+dxzyaW62gkEoHXGXZzMzunzPhv3jvvvANzVrTDfqfM8PXdtV/1Fx8REREJDU18REREJDQ08REREZHQ0MRHREREQkMTHxEREQkNrxKmIAhgVQCruHjzzTfpugoXLgzz22+/HeaxVFv5tppg1QhsPatWrfL+TE2bNvV6f968eelrsXwnqCoAtekwM/v222/peqpXrw7zV199FeZJSUnn8On+Uyx9vNgxyowdO5a+tmHDBphXqFDB6zOx3ldm/DxgEhISrECBAlE5azPx0ksv0XWx6gl2Dvput5n7+PXBqhtd15i33noL5o0aNYrLZzKLrVdgEARej/4fPHgwfa1q1aow79ixo9dnYj2/zHDlpau6iFXHst5wX331FV3XjBkzYO7bW8xVHevTf9KMX2NYFfPo0aPputjx869//cvrM7EekGZmxYoV81qX2W/b6FNBxlqnuNxxxx1e72fzDDPcosX1+fUXHxEREQkNTXxEREQkNDTxERERkdDQxEdERERCQxMfERERCQ1NfERERCQ04tKRc+fOnTD/5Zdf6DLdu3eHealSpeLxkWLCmngyP//8M32tc+fOMHeVHSKs5DieYmmUecstt8CclZmWLFnSe4xYBEEAPwNrpPvll1/SdbGyZ9aYcu3atTBnDVLN4rd/s7OzvZepV68ezFFp6P9thw8fhrmrrJmVerNmmVWqVPH+XLE0jTTDzR63bt0K38u23cysbt26MJ8yZQrML7vsMpi7rruxbuN/Y41CXY2K2THK7N+/H+axNCL1xX4HXTp06ABzth3sehGvx0b8n9C5xa5xria3Tz75JMzZ8V6+fHmYx3J+MvqLj4iIiISGJj4iIiISGpr4iIiISGho4iMiIiKhoYmPiIiIhEZcqrpYs0xXY8qJEyfC/JtvvoH5jz/+CPOKFSvSMWKpdEG+//57mL/88st0maysLJiPGzcO5iVKlID5d999R8dgjUJ9sYoAV8XRmDFjYM4ano4fPx7mrkarefLkoa+5oGqENWvWwPcuX77ce/0fffQRzBcvXgzz++67j64rXlWMZcuWhbnr/MifPz/MP/74Y5iz6r8rr7ySjhGvar4jR47AfPv27XSZFi1awJwdc127doX5vffeS8dglWOxYM1sXddRdm2aPXs2zPv16wdz1pjWDDdpjqVKqnLlyjC/+uqr6TLDhg2DOWs6yq6JjRs3pmMcOnSIvuaDHev58uWjy2zevBnmzz//PMwfeOABmLuaHbvG98XOw9q1a9Nlpk6dCnPWfHfQoEEw79WrFx0jJyfnnLIz9BcfERERCQ1NfERERCQ0NPERERGR0NDER0REREJDEx8REREJDe+qLnSnNKsOOXnyJF3Pjh07YM4qjEaNGgXze+65h47Ben74YtVFrqqnokWLwrxWrVowZ1UKn3/+OR2DVWgwOTk5sO8Pqyxi/WLMeG8Wdnf//fffD3PW08zMrG3btvQ1X2wfJicn02UuuOACmLdv3x7mrIpg5syZdIxYKvPQOKyi5NSpU3Q97DupUaMGzFlFCatAMXOfn0gkEoGfOZbviZ2DEyZMgDmrHO3bty8d46effvL+XJFIBPatKlasGHw/6w1nxo9Fdk1OT0+HOTvWzcx69+5NX2NQRS0711x9nnbv3g3zyy+/HOZsu1999VU6xtChQ+lrSE5ODtwn5cqVg+93VcCx83P9+vUwZ5XEnTp1omM0bdqUvsawY7RAgQLw/ez33MysUqVKMC9TpgzMJ02aBHNXPzJUkenqMae/+IiIiEhoaOIjIiIioaGJj4iIiISGJj4iIiISGpr4iIiISGh4V3UlJETPlVi/muuvv56u5+uvv4Y5q2DIzMyE+dKlS+kYxYsXp6/5aNasGczHjh1Ll2FVTOwOf1YN5epX5aqGQIIggNUbrPqtYMGCdF2oOszMbMOGDTBn/ZGuuOIKOka8eq2ZmVWrVg3mPXv2pMuw3ltsn7BKDHTOnOHbJygSicDvhVWU1KtXz3tsdk6xc3Dbtm10DFdVGYOq1lgFCKs0MzMbMmQIzFll5SeffAJzdhyY8d5FLkEQwGOodOnS8P1XXXUVXdfq1athzr6vrVu3wtx1rUTVnWc7N1G/PFZx5aqOnTVrFsxZFdOLL74Ic9Z/zszs73//O30NSUhIgNfRtLQ0+P5GjRrRdf3yyy8wv/DCC2HOKqVdPetiuY6yY5T91t922210Xaw/JftNYNeThQsX0jGuu+66qIz1FjTTX3xEREQkRDTxERERkdDQxEdERERCQxMfERERCQ1NfERERCQ0NPERERGR0PAqZ49EIrCcLl++fPD9zz33HF0Xa+j42muvwTwrK4t+JoaVy/liJausmaOZWcuWLWHOtq9NmzYw7969Ox2DlTwyrJw9KSkJvv/gwYN0XaxEc968eTCvX78+zFkJqFn89p8ZP0769OlDl3n33Xdh3qtXL5iXLVsW5s888wwdw/XIACQIAvi9sAaXria3f/vb32A+cOBAr8/EGkaameXOndtrXewYZSW5r7/+Ol3XqlWrYF6iRAmYs9J71hjSjDdtjAUqATcze+utt+gyrNSdlRCz8+3hhx+mY6DrDPusZr9d248ePRqVs3Pw7rvvputiTVjZIwkY1yMBXGXPPgoVKgRzVyPb1q1bw/z777+HOXv0CGvIaxb7dRTtL9b4k11LzMyWLVsGc9cjBpAePXrQ11DpvesxIvqLj4iIiISGJj4iIiISGpr4iIiISGho4iMiIiKhoYmPiIiIhEbgqoqKenMQ7DGzzb/fx/nDpEYikajSDm3feQNun9mffxu1feeNP/sx+mffPjMdo+f7NvLt85n4iIiIiJzP9F9dIiIiEhqa+IiIiEhoaOIjIiIioeH1LOukpKQIeuQ5u0/I1fIgMzMT5vv37/f5SM6WB6ylw9KlSzPRTU9JSUmRlJSUqPezR1+7HnW+bds2mO/duxfmpUuXhnnx4sXpGOjR/mZm6enpdPtc39d/O3ToEH3t2LFjMN+5cyfMWeuCSpUq0THQY8jN+PaZ+W/jiRMn6GusTYrvMVqmTBn6GnvM/ZIlS7z2ITsHjx8/TsfeuHGj9zIIe4y+GT8HV6xY4bV9rMUNaqFzxpYtW2DOjmv2OH7X9rFWAewaY+a/D9lxaGa2ebPf/acXXXQRzPPnz++1noyMDMvMzIRfmO/27d69m47DjkXXd4JUq1aNvsbajixatCgu56Drd5BtB2r5Ycb3U3JyMh2DtZRi22f22zampqZG5ewccVm7di3M2XnIftcqVqxIx0DbuGXLFnqMek180tLSbOHChVE563Hzww8/0HW9/fbbMHf1FkJc/cCuu+46mJcoUQJeLVJSUmzWrFlRed68eeF62OTNzKxv374w/+ijj2DO+tW4enWx3lC5cuWC28f2H/Pzzz/T15YuXQrzAQMGwJz9+H/66ad0DDYpSkxMpFd7to3sh5P9+JuZffjhhzD/6quv6DKI6xht1qwZzIsWLeq1D9kEbt26dXTsW2+9FeYrVqygyyBPPPEEfY2dgxUrVvTaPvZDsHXrVjo2O6emTp0Kc9bTiJ3LZmYdO3aEecmSJZ3HKOppx66jrp5Gd9xxB30NGTt2LMzr1q3rtZ569erR19g+ZJOYoUOH0nWxY3H06NFn+YT/if3emPFec7lz5/Y6Rtk/hKdMmULHZtuxaNEimLP95DoHL774YpjnzZuXHqOpqalev4Uuvv3I2CTOtc/RNjZp0oS+X//VJSIiIqGhiY+IiIiEhiY+IiIiEhqa+IiIiEhoeN3czGRkZMCc3c1txquYBg0aBPNRo0bB3FV5VLBgQfoakpCQAO8OZ2O4bspbtWoVzKtUqQLzPXv2wNy1DeyGXdf7UTUWWw+rBjD77eY3ZODAgTCfMGECzNn3ZGZWrlw5+ppLdnZ2VJaYmAjfy6rszHg135AhQ2D+wgsvwJzdqGhm1qpVK/qajw0bNsC8X79+dJnKlSvD/JZbboH5M888A3PXTf6uahMfrJqFFQuYme3atQvmzz77LMwHDx4Mc3ZumvGqrrNBxyM7Fl9//XW6HlatxG5Cff7552HuKjJg1ZW+WLHL3Llz6TI33XQTzNE5bsYLElyVY+ymcl/s5nhXlWTNmjVh/vDDD8P8qaeegvl3331Hx6hduzZ9jQmCAB5D7LewW7dudF3sJmZ2jLJqTFYZbIav1a4KNP3FR0REREJDEx8REREJDU18REREJDQ08REREZHQ0MRHREREQsO7qgv1I2GtE9q0aUPXwx4TzlohsMfrt2zZko7B7rL3xarTXO0fHnroIZiPHDkS5qy1AKtGMuNVR673ozvp2d3vl156KV0X6zFTqlQpr3WxY8f1uc7GZzlXjyLWToI9rp89sp5VT5nxvjS+WEuH5s2b02UefPBBmLMqG1bVdfXVV9MxXJWB8eCqqmIVPuz4YJWHtWrVomPE6xpjxqtcevXqRZe5//77Yc6qf7755huYHzhwgI5RsmRJ+poP1suqU6dOdBlWYfjjjz/CnPVzatGiBR3j9z5GXb9R7NwpXLgwzNl5znrimfn/Triwa4OrZxyrruzSpQvMf/rpJ5iz1htmuOJLVV0iIiIipomPiIiIhIgmPiIiIhIamviIiIhIaGjiIyIiIqGhiY+IiIiEhnctJioRYyW5rNmYmdkTTzwB84MHD8L8vvvug7mrnNS3iSfDSvVYSbcZb0w3depUmLOSQ1YKaMYbFDKsSSkr6X7vvffoul566SWYp6SkwLxSpUowZyW8Zrw8/GxQ2SzabjO+P8z4YwzGjRsHczaGq2Te1cDQB/se69Sp472uESNGwJw9guLIkSN0XSdPnvQeH9m0aRPMXcfPihUrYP7222/DnJ1rrmtMrMcowpq9uh5JwLCmlazE19VoFj0ygJWmuyQlJcF85syZdJkePXrA/IMPPoD5Y489BnPXYw/YectEIhF4XLPfQdZA2Iw3wE1PT4c5+81h5e9mZocPH6av+WLrcj26hjXaZmXraWlpMHc1KfX1/7V3p1FSlGcbx+/uEXABZBl2mAFk16OBCKhAWCIEkACSEJGoqDkEEMliDh6NMUZZTNCDUXJUMJG4h4Qo5kTESBAJBFkECYoiCMMiIDuyitD9fniPH+Lc1zPztK0nUP/fx6uq6+marqp+aOqum198AABAYjDxAQAAicHEBwAAJAYTHwAAkBhMfAAAQGLkpcOeqnqYOXOmfI1qRqru6FbVXqEmj7k0EPSqFVQFQ40aNeR2JkyYEDWuqkBbtmyZfE1xcXHUGOl02q0wUp9FqKpL/U3WrFnj5gsWLHDzUaNGyTFUNUBZvMaue/fuddedO3eu3M6rr77q5qoK5Pvf/76bhxoknnPOOXJZDNXsVVW/mJndcccdbq6qJ/r27Ru1vln+KitVNYs6rsz056cqmNS1J3Se59JIN5PJuM0m//jHP7rrz5gxQ25r27Ztbn7w4MGo96SaT5qZtWjRImpbSqtWrdz8+eefl68JHb+emjVrRq1vFq4M9KRSKfd7R1XSTZkyRW5r+/btbr5ixYqo93TZZZfJZaGKr1hVqlRx80qVKsnXqMaxSklJiZvPmjVLvqZr166lspMnT8r1+cUHAAAkBhMfAACQGEx8AABAYjDxAQAAicHEBwAAJEZ02ZNXpaH6TPXv319uR/UvUZUxN954o5uru+LNcq+4+LxmzZq566q+MGZmP/zhD91cVY6o/e7SpYscI7YaQVF35Ks+OWZm/fr1c3PVH+m6665z83379oXfXA68u/nVMarel5lZ27Zt3VxVFwwdOtTNq1WrJseIpSqCVD+wUOWf6lk1duxYN//5z3/u5qpiziz+GM1kMm4/IFVZdc0118ht7d+/383nz5/v5g8//LCbd+7cWY4RqhwJ8a5NzZs3d9cN/X1V9Zbq0dauXTs3V33YzPzq2NC1NZvN2qeffloqV8foTTfdJLe1aNEiN1d9IM8//3y5LSX2e0L16jrrrLPc9b2Ko8906NDBzYcNG+bmjRo1cvPYyqmynDx50q2kVt9foWN0586dUWOrc7pJkybyNV4vNq+69zP84gMAABKDiQ8AAEgMJj4AACAxmPgAAIDEYOIDAAASI6qqS93Nrvpl1a5dW25L9RYKVYJ5Qv2ccqnq8u4Ev+iii6K3o/rbqLvyx48fHz1GvhQVFUXlZvrzW758uZt37NjRzUPVCIcPH5bLQrzPsF69eu66qvrFTFcSqf5aoQo8xatgyoWqzGvfvr18jVcdZqartxTVty0X6XTaPafVeR46fn7729+6ea9evdy8T58+5XiH/y1UOaKk02m3AmjAgAHu+qpPoZnZLbfc4uaqP9Po0aPdvE2bNnKMWKlUyv27nDhxwl0/VBk3ZMiQqNdcccUV5XiHX4zq1aX6ZYXOD/U9UbduXTcfNGhQOd7hf1PVjSEFBQXuOaeOK1X5bGZ21VVXufmVV17p5qo/W67fBx5+8QEAAInBxAcAACQGEx8AAJAYTHwAAEBiMPEBAACJwcQHAAAkRlQ5eyqVcpsOqgZla9eu1QM7je/MzPbs2ePmqtlhlSpV5Bj5osoRt27dKl/TsmVLN48t1/8qqP1T5c5mZvfff7+bv/76626u9jtUBplPqhQyVOqp9qWwsNDNVePdhg0byjG85noh6XTabfaomlUeO3ZMbuub3/xm1NiKGtvMrGbNmnkZQ+2Haoprpt/X7Nmz8/Ke8k09JkFdE83MPvnkEzf/zW9+4+aqSWm+eU2BVQn6Y489JrejmhiPGjWq3ON+VbzGrGZmGzdulK+ZOHGim19++eVu/tOf/jT6fYUe+RKSr79ljx493Py2226LGjef3/X84gMAABKDiQ8AAEgMJj4AACAxmPgAAIDEYOIDAAASIxXTYDCVSu0ys01f3tv5yhRns9lanw/Zv1OGu39mp/8+sn+njNP9GD3d98+MY/RU30e9f/nsrAwAAPC/jP/qAgAAicHEBwAAJAYTHwAAkBhRLSsKCwuzjRs3Lvf66nHjZmYbNmxw86pVq7q5erS/Wt/MrEKFCm6+YsWK3d5NT2r/1KPIt23bJsdWj9hXj21PpVJuXrduXTnGueee6+YrV66M2j91n9fOnTvl2OqzrVatmpuH9iPWm2++6e6fmd7HEydOuNvK5TNUj1RXx1utWu5bNTPdiiVfn+H27dvl2Kqlg2ono/YjdA4q6jOM3b+PP/5YjrF+/Xo3r1ixopvXqFHDzUP7p9pMqM/PTO9jJpNxtxX6DHfs2OHm6lhU7VPUvislJSW2e/du96IVew5u3rxZjqOuM2eddZab16tXz83VdclMX3vzdYyqz8hMtyNRbSbUOaiOw5BcrqPqGFVtq8z08auuffXr13dzr1VPyKZNm+QxGjXxady4sS1fvrzc68+YMUMuGzJkiJt36tTJzb/zne+4eajfkDrJK1So4N6trvZPfXB33323HPudd95x80OHDqn35Oa33nqrHKN3795uXqVKlaj9O36G+AhxAAAWeElEQVT8uLudhx56SI49a9YsNx8wYICbjx07Vm4rViqVktUGah/ViXnXXXfJcdasWePmqmdMnTp13Fz1FTLTPd3OPvvsqM9QTc5VLyAzs7lz57p57dq13XzkyJFu3rNnTzmGoj5DtX+qJ9U//vEPOYY6FtWF9eqrr3Zz1TfJzKxjx45uXrly5ehjVF0bQp/hvffe6+bqMxw/frybDx06VI7hufjii+Wy2HNwxIgRclszZ850c3Xe3HHHHW4+cOBAOYaa6Mceo+o6+utf/1qO/cwzz7j5JZdc4uajR4928w4dOsgxlFyuo+oY/fOf/yzHGTdunJu3bt3aze+88043D/WZKygoKJWpc9OM/+oCAAAJwsQHAAAkBhMfAACQGFH3+MSaOnWqXKZuklb3Q/Tv39/Nn3rqKTmG+j/7WOqmvNANgeomO3VTnrrRNHTjn7oBTslkMu446p6V0PZr1qzp5itXrnTzyZMnu/ngwYPlGI0aNZLLlGw2694P8sYbb7jrb9myRW5L/R+x2kf1f/zqhkAzfTwomUzGDh8+XCo/evSou766N8bMrHPnzm7+3nvvubm63+xPf/qTHKNFixZyWYxKlSq5+erVq+Vr1M2m1113nZtPmTLFzdX5YWbWo0cPuSzWsmXL3Fzdx2Omr6Pqfhp1v0nsPT65eP/9991c3cdjZta8eXM3LykpcXN1v1CvXr3kGLE352ezWbfwQd3XuXTpUrktdfyoe2nVva4LFy6UYxQVFcllsdR3wv79++Vr1A3q6jqqjnd174+ZWfv27Utl6qZ1M37xAQAACcLEBwAAJAYTHwAAkBhMfAAAQGIw8QEAAIkRVdWlKmZUxYW6I99MV5T07ds35i25T2z8TOiubk82m3WfgKuqi37yk5/IbakqJnVXfGFhoZs3adJEjhErlUrJx/V71JOvzfQd+erJon//+9/dPFT1ExpfSaVS7pNY1X537dpVbktVBakqH7UvqsIvNIaSSqXc8009sr5bt25yW6qaRr3fFStWuLmqKDPL7RyMucaEnqq8ePFiN+/Xr5+b/+Uvf3HzULuDfFJPiA+1CfrVr37l5uqJwOopxV8F1V6kVatW8jWqAk9V8/3nP/9xc68S8jOxVV3qHFQVmqHuAqoNgzrXtm7d6uah63rsOWj2/9Wj3nmt9lFVm5mZPfLII26uvlfVk9VjK2BD+MUHAAAkBhMfAACQGEx8AABAYjDxAQAAicHEBwAAJAYTHwAAkBjR5eyhhoufF2rgN2TIEDd/4YUX3HzgwIFufv7558sxYsv4UqmUVahQodzrq6aUZmb//Oc/3fzCCy90c1XCd/LkyZzG96hyfVUqvHHjRrkt1dxTNeRTJcGh4yl2/z7jPeKgbt267rqq7NfM7MUXX3RzVUKtHj2wbt06OUao0a1HlXurMmXVONHM7LHHHnPzZs2aufmwYcPcPFRKGyp1V9Lp8v97rEOHDnLZggUL3FyVSKtjJNQsN/ZxBCHqcQjt2rWTr1HXy02bNrn5fffd5+ah8zDm8whRjzdp27atfM3jjz/u5k2bNnXzH//4x26+Z88eOUadOnXkMk82m3UbV7dp08ZdXzUcNTN78MEH3VyV699+++1uHvre8q75ZVGPBVGKi4vlMrUd9QgO1VxcrW8Wfx7yiw8AAEgMJj4AACAxmPgAAIDEYOIDAAASg4kPAABIjKiqrnQ6HdUoLJe7yd9++203V3e/qyqpr8LatWvlMtWEVd19ryo61HZykU6n3Sapq1atctdfsmSJ3JZqIPrBBx+4+W233ebm/fv3l2PkU6gZqtKyZUs3V5UVqjpl3759cgxVUaek02m3umHHjh3u+rNmzYravpmu8FEVMzVr1oweQ1GVlarCT1X9mOmmmCrv3r27m4eqU3NpAKmoysfQMfLcc8+5udoXlR84cECOUb16dblMCVWjfl6oIkdVBV555ZVuPnz4cDdXn7lZfNVabPXv/v375TLVjFQdCxMnTiz3uF+E2kevms3M7Mknn4weQ33uF1xwgZvn8zrDLz4AACAxmPgAAIDEYOIDAAASg4kPAABIDCY+AAAgMaKquk6cOOH2PFF3W8+bN09ua/bs2W7+7LPPuvmMGTPcXPW4MjMrKiqSyxSvomXXrl3uuuedd57cjqoieuKJJ9x85MiR5Xh3/y2XXlZetcXBgwfdddesWSO3M27cODe/55573Pzhhx92c9WzzSz3Xl0eVY3Qvn17+ZoNGza4+bvvvuvmqqorl6oYRfUJOnLkiLv+5s2b5bYGDx7s5ocOHXJzVUE1duxYOUZsD52TJ0+6VXCqSkhVxZiZTZo0yc3Vsah6AYUqeELVQkomk3E/rypVqrjrq+PNTFeVqcoYVTV76aWXyjFiZTIZtxpL9WxatGiR3Fa9evXcXFUxqgrViy66SI4Re4xms1n32qSqw+bPnx+1fTOzqlWrurk6D7z+hF+E6uuoesCp676ZrgBW59vixYvdvF+/fnIM73wK9p+TSwAAAE4zTHwAAEBiMPEBAACJwcQHAAAkBhMfAACQGFFVXWeccYZbwaV6cr300ktyW6oXyfr1691c9TsZOnSoHEPdNR7i3Zl/5plnuuu+8sorcjuqP9OHH37o5oWFheV4d/8tpl/MZ7y7/xs3buyuq+7gNzNr1KiRm2/cuNHNt2zZUvab+xxVTReiKmb27t3rrr9w4UK5reLiYjeP6VeXb6lUSlbHeEpKSuSyX/ziF24+bdo0N1fVFiGhPmWegoKCqCq4UJ+l1157zc3V30RVYobOM9VLqixeNZa6jm7btk1uR1Uk7d69283V9SdYARPZy0q9Rv2tQtcGdd1XVZqq0jZU1RXbby2VSlnFihVL5Vu3bnXXV8ehme4Dpyqlp0+f7ua9e/eWY5x99tlymaJ6dalrn6qyM9MVZ+vWrXNzVQUW2kfveAhV6/GLDwAASAwmPgAAIDGY+AAAgMRg4gMAABKDiQ8AAEgMJj4AACAxosrZFVXuqZoBmpl997vfjRrj5ptvdvNWrVrJ15x77rlRY5j5TeBUmenLL78st7N27Vo3f+ihh9xcNaULybWU9vNU+WCo+eTdd98dNYZqcKnKUs1yK8NMp9NWqVKlUnkuJejqMQaqnFw1Cg01sqxbt270+/I0adLEzUOf4Zw5c9xcNTYdPXq0m4eOwxo1ashl+dCnTx+5bODAgW5+9dVXu/nw4cOjx8/1kRne8agaLqv3a6bLm2vVquXmqqw7tlFnSDqdds/dZs2aueuHPkN1je3SpYubX3vtteV4h1+OBg0auPmoUaPka1avXu3m6rEgqglr6JELob9vrDp16rj5lClT5GvUPECVuavPVj2iwcyscuXKpbLQYwr4xQcAACQGEx8AAJAYTHwAAEBiMPEBAACJwcQHAAAkRirmbv5UKrXLzHTnylNHcTabLVX2wP6dMtz9Mzv995H9O2Wc7sfo6b5/Zhyjp/o+6v3LZxkjAADA/zL+qwsAACQGEx8AAJAYTHwAAEBiRLWsKCwszBYXF5fK1aOht2/fLrelHuOvWgs0atTIzUOPpVbefPPN3d5NT4WFhdmioqJS66fT/vzw8OHDcgzVsqJly5Zurh59/8knn8gx1GPKV65cmZf9279/vxx7165dbq5ab6hHnedCfX5m8cdoqGWGat2gjtHq1au7eSaTkWNUrFjRzVetWiU/w5j927t3rxxbfYZqP2rXri23FSt0DjZu3LjU+upexJKSEjnGgQMH3Fy1slHHbqj1jWpfUtYx6u2j1y7HTH9OZmZ79uxx82PHjsnXeJo2bSqXeX+XzZs32549e9yDrmbNmu4xqq4zH374oRz74MGDbl5YWBiV5yL2GFV27twpl3300UdurvajXr165R63LLkco+papvbDzGzbtm1urr7T1XVGtY4y88/DTZs22e7du91jNGriU1xcbP/+979L5eoLeMKECXJb8+bNc/PWrVu7+QMPPODmXl+msqRSKfdu9aKiIlu0aFGpXH3RvfHGG3KMrl27uvkTTzzh5h06dHDzdevWyTFUn6eqVavmZf9eeOEFOfbUqVPdvGfPnm7+s5/9TG5LUV926XRaVhsUFxfbkiVLSuXqCyr0pfKjH/3IzdUxetVVV7l5aILsTUTNzGrVquXuY3FxsfsZqr5izz33nBxb9dD53ve+5+ZjxoyR24qlzsHGjRvb8uXLS+XqonfjjTfKMWbPnu3m3/rWt9y8d+/ebt63b185hvqCUvtn9v/7uHTp0lK5mqg9+uijcvwnn3zSzd977z35Gs/EiRPlMu/v1b17d7l+cXGxvf7666Vy1XvvrrvuktuaO3eum48YMcLNb7jhBrmtWLHHqJoU/O53v5NjPPjgg24+bNgwN//lL38ptxWrrGN02bJlpXI1ob7//vvlOOo933rrrW6u+nLu2LFDjlGtWrVSWadOneT6/FcXAABIDCY+AAAgMZj4AACAxGDiAwAAEiPq5uZMJuNWGXk3W5qZTZo0SW5L3ez68ssvu7m6SfP666+XY8Q+lTqdTssbfT1jx46Vy44fP+7m6oZLdXNzqHpA3VQe4t2Ap26gfuSRR+R2VLWFulmvW7dubv71r39djpFLxZ6iKmb++te/ytf861//cvO33nrLzdu0aePm7dq1k2PEVqFks1l3X7wbus3C56CqVlq8eLGbX3PNNW6uqsBykclk7OjRo6Xy+fPnu+s//fTTclsjR4508w8++MDNJ0+e7ObqZu8vwqtwevHFF91177nnHrmdVq1a5eX9NGjQQC7zqroKCgrk+tls1r32qkrXp556Sm6rfv36bj5u3Dg3VwUG6sbqXKhjVH13zJkzR27Lq34zM5s+fbqbq/Ng2rRpcoxmzZrJZSHe9Vd97qpYKUTdmK8+K1UwZOYX+oS+P/jFBwAAJAYTHwAAkBhMfAAAQGIw8QEAAInBxAcAACRGVFVXQUGBe4e/9/h1M7NDhw7JbfXp08fNVRsIdZe7erS3Wbi3hyeTybjvWfWYCbWTqFGjhpurO9Y3bfKfHh66Mz22/5WqWlNVLqqfmplZkyZN3Fw9Kl+1v2jbtq0cI7Yq77PXeJWHaluhMRo2bOjmqoJq4cKFbh6qRlDVZko6nXb7uqnPUPXJMdPnoNeWxkxXXA4dOlSOEdszSh2j6m8eMmjQIDefOXOmm6v9DvWsy2dvKHUNGDJkiHyNqmJSn+03vvENN+/cuXMZ7678CgoK3GN0/fr17vqh64y6jqqq0ldffdXNBwwYIMeIPUZTqZT8TvBcdtllcpk6b9V1X1VPbdiwQY6RS1VXJpOxI0eOlMrV91foGFXVx/v27XPzBQsWuPnFF18sx4iu4I5aGwAA4BTGxAcAACQGEx8AAJAYTHwAAEBiMPEBAACJwcQHAAAkRlQ5u5nf5FI1OwxRjRC3bt3q5lu2bHFzVUpvpht/Kul02ipXrlzu9X//+9/LZapkdtmyZW6+cuVKN7/pppvkGEVFRYF3V36qLD7091PlnF6zODOzWbNmuXm/fv3kGJdccolcFnpfXjm0er+q7NdMNylVn9Uzzzzj5qF9vPzyy+WyGKqZbehxAapp5IoVK9z8b3/7m5v37t1bjqHKkUO8a4wqZa1Xr57czpgxY9xcPUJAnQeqDNtMH++56NGjh5tv375dvubee++NGuP222+PWj9XXjl27dq13XW/9rWvye2oMm3VEFT9PUKP/oi9zqhGwUqoye2jjz7q5uqxIErosRW5SKfTVqlSpXKvP2LECLlMNVZVpfzvv/++m5eUlMgxLrzwQrnMwy8+AAAgMZj4AACAxGDiAwAAEoOJDwAASAwmPgAAIDGiqrrU3eytW7d217/vvvvkti699FI39yo6zHST0lCj0I4dO8pl+RCq1lHL3n77bTf/wQ9+4OahipILLrgg8O58XnWTqvwJVQQpGzdudPNvf/vbbh5qPtmuXbvo8c10BZdHVUOZmT377LNuro65Tp06ublqvGuWW+WaRzVCnDNnjnyNqk5r06aNmy9atMjNQ5+haooZ4n1+6nx69913o7evmiY+/vjjbu41vf0ydOnSxc13794tXzN16lQ3V81LVeXYrl275BjVqlUrlZXVFNKr6lLH+muvvRbclkc1wFbVPepYN4v/nlCVoydOnHDXb9GihdzW5MmT3fyVV15x8wceeMDNQ9WNuSooKMjLdv7whz+4+ezZs91cVT5XqVJFjqHmDQq/+AAAgMRg4gMAABKDiQ8AAEgMJj4AACAxmPgAAIDEiKrqSqVSbkWE6hlVv359ua2DBw+6uboDvkGDBlF5rry7w2OqhMqiKrFGjRrl5qHeOldccUVe3pOq0PAqM8rSpEkTN+/Vq5ebq34tZrqn0lfl448/dvPmzZu7+fPPP+/m48aNk2OEerF92c455xw3v/nmm938jDP8y4Xq4WVm1rNnz6j3lM1m7fjx46XyihUruuvn0idQUf2RzjvvPPmaXI7RbDbrVoqp3khnnnmm3JaqiLrzzjvdXP0da9WqJcfw9rGsa0Mu144YqqeiOh5C1bFHjx6NGltVN6ueaqrS1UxXPR47dszN16xZ4+ahqiZVAVcWbx9Vpdenn34qt7Njxw43b9iwoZur/n6hXl1ev7fQuckvPgAAIDGY+AAAgMRg4gMAABKDiQ8AAEgMJj4AACAxoqq6lMLCQjcPVXuou+9Vn479+/e7eewd+WWJqeAK9QlTvalUxcykSZPcXN0Rb5bfajNPqIeOWqZ6X7300ktuHupVpSpQyhJTmXfkyBG5neuvv97Np02b5ubqb3L48GE5RtWqVeWyfFi9erVc9vTTT7u5qsSaOXOmm4cqeHLpc+VVGaoKu+HDh8vtDBgwwM1VXyp1vVLbMcutn1Emk3GvW6oyZ968eXJbqiJT9azKRb56Nqkqm7lz58rXqOv7rFmz3Pytt95y8z59+sgxYq8zqVTKrXBU32njx4+X27rlllvc/Nprr3VzVQ2t+s+ZmVslWR7e566Ot1Dlquo7VrduXTdX18RQTzXv8whdl/jFBwAAJAYTHwAAkBhMfAAAQGIw8QEAAInBxAcAACQGEx8AAJAYeSlnV80O33nnHfmaVatWufmePXvcXJXYNm3aVI6hGr2FeCWXqgGbKu0zM1u7dq2bjxkzJur93HDDDXLZ5s2bo7alqP0LlWGrxw5MmDDBzVVDus6dO8sxdu7cKZeFeKXrqiw21NyvevXqbt6tWzc3V5+HKlk1M/voo4/kshiqbFw1NTTTZdLq0QqKaohpZnbgwIGobaVSKbdZp2qQGipFVudO7dq13XzIkCFu3qpVKznGiRMn5DKloKDALX1WzSRVibaZWdeuXd28e/fuUe8pdK0MNUmNof5WS5Yska+ZPn26m6uGlV26dHHzvn37yjHUd04sVYY9aNAg+Rr1OAZVtj548GA3V6XhZvpRMLlQ15nQebh06VI3V48+UaX8qjm0mdm2bdtKZaEyfn7xAQAAicHEBwAAJAYTHwAAkBhMfAAAQGIw8QEAAImRClUmlVo5ldplZpu+vLfzlSnOZrO1Ph+yf6cMd//MTv99ZP9OGaf7MXq6758Zx+ipvo96/2ImPgAAAKcy/qsLAAAkBhMfAACQGEx8AABAYjDxAQAAicHEBwAAJAYTHwAAkBhMfAAAQGIw8QEAAInBxAcAACTG/wGJE5IQhOfmTQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "components = pca.transform(example_digits)\n",
    "filtered_digits = pca.inverse_transform(components)\n",
    "plot_digits(filtered_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}